From Tealeaves Require Import
  Classes.Coalgebraic.TraversableMonad
  Classes.Coalgebraic.DecoratedTraversableFunctor
  Classes.Coalgebraic.DecoratedTraversableMonad
  Adapters.KleisliToCoalgebraic.TraversableMonad
  Adapters.KleisliToCoalgebraic.DecoratedTraversableFunctor
  Adapters.KleisliToCoalgebraic.DecoratedTraversableMonad
  Classes.Kleisli.Theory.DecoratedTraversableMonad
  Classes.Kleisli.DecoratedContainerMonad.

From Tealeaves Require Export
  Theory.DecoratedTraversableFunctor
  Theory.TraversableMonad
  Classes.Monoid
  Functors.List
  Functors.Subset
  Functors.Constant
  Classes.Categorical.Applicative.

Import Product.Notations.
Import Monoid.Notations.
Import Batch.Notations.
Import List.ListNotations.
Import Subset.Notations.
Import ContainerFunctor.Notations.
Import DecoratedContainerFunctor.Notations.
Import DecoratedTraversableMonad.Notations.

#[local] Generalizable Variables M U W T G A B C.

(** * Theory of Decorated Traversable Monads *)
(**********************************************************************)
Section decorated_traversable_monad_theory.

  Context
    `{op: Monoid_op W}
    `{unit: Monoid_unit W}
    `{Monoid_inst: Monoid W}.

  Context
    `{ret_inst: Return T}
    `{Map_T_inst: Map T}
    `{Mapd_T_inst: Mapd W T}
    `{Traverse_T_inst: Traverse T}
    `{Bind_T_inst: Bind T T}
    `{Mapdt_T_inst: Mapdt W T}
    `{Bindd_T_inst: Bindd W T T}
    `{Bindt_T_inst: Bindt T T}
    `{Binddt_T_inst: Binddt W T T}
    `{! Compat_Map_Binddt W T T}
    `{! Compat_Mapd_Binddt W T T}
    `{! Compat_Traverse_Binddt W T T}
    `{! Compat_Bind_Binddt W T T}
    `{! Compat_Mapdt_Binddt W T T}
    `{! Compat_Bindd_Binddt W T T}
    `{! Compat_Bindt_Binddt W T T}.

  Context
    `{Map_U_inst: Map U}
    `{Mapd_U_inst: Mapd W U}
    `{Traverse_U_inst: Traverse U}
    `{Bind_U_inst: Bind T U}
    `{Mapdt_U_inst: Mapdt W U}
    `{Bindd_U_inst: Bindd W T U}
    `{Bindt_U_inst: Bindt T U}
    `{Binddt_U_inst: Binddt W T U}
    `{! Compat_Map_Binddt W T U}
    `{! Compat_Mapd_Binddt W T U}
    `{! Compat_Traverse_Binddt W T U}
    `{! Compat_Bind_Binddt W T U}
    `{! Compat_Mapdt_Binddt W T U}
    `{! Compat_Bindd_Binddt W T U}
    `{! Compat_Bindt_Binddt W T U}.

  Context
    `{Monad_inst: ! DecoratedTraversableMonad W T}
    `{Module_inst: ! DecoratedTraversableRightPreModule W T U}.

  Context
    `{ToBatch7_WTT: ToBatch7 W T T}
    `{ToBatch7_WTU: ToBatch7 W T U}
    `{! Compat_ToBatch7_Binddt W T T}
    `{! Compat_ToBatch7_Binddt W T U}.

  Context
    `{ToSubset_U_inst: ToSubset U}
    `{ToSubset_T_inst: ToSubset T}
    `{! Compat_ToSubset_Traverse T}
    `{! Compat_ToSubset_Traverse U}.

  Context
    `{ToCtxset_T_inst: ToCtxset W T}
    `{ToCtxset_U_inst: ToCtxset W U}
    `{! Compat_ToCtxset_Mapdt W T}
    `{! Compat_ToCtxset_Mapdt W U}.

  Context
    `{ToCtxlist_T_inst: ToCtxlist W T}
    `{ToCtxlist_U_inst: ToCtxlist W U}
    `{! Compat_ToCtxlist_Mapdt W T}
    `{! Compat_ToCtxlist_Mapdt W U}.

  Context
    `{ToBatch3_TU: ToBatch3 W U}
    `{! Compat_ToBatch3_Mapdt W U}
    `{ToBatch6_TU: ToBatch6 T U}
    `{! Compat_ToBatch6_Bindt T U}.

  Import
    Kleisli.TraversableMonad.DerivedInstances
    Kleisli.DecoratedTraversableMonad.DerivedInstances.

  (** ** Relating <<toBatch7>> to <<toBatch3>> and <<toBatch6>> *)
  (********************************************************************)
  Lemma toBatch3_to_toBatch7 {A B: Type}:
    forall (t: U A),
      toBatch3 (B := B) t =
        mapsnd_Batch (B1 := B) (B2 := T B) ret (toBatch7 (B := B) t).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
forall t : U A,
toBatch3 t = mapsnd_Batch ret (toBatch7 t)
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
forall t : U A,
toBatch3 t = mapsnd_Batch ret (toBatch7 t)
    intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
toBatch3 t = mapsnd_Batch ret (toBatch7 t)
    rewrite toBatch3_to_mapdt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
mapdt (batch (W * A) B) t =
mapsnd_Batch ret (toBatch7 t)
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
mapdt (batch (W * A) B) t =
mapsnd_Batch ret (binddt (batch (W * A) (T B)) t)
    rewrite mapdt_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
binddt (map ret ∘ batch (W * A) B) t =
mapsnd_Batch ret (binddt (batch (W * A) (T B)) t)
    compose near t on right.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
binddt (map ret ∘ batch (W * A) B) t =
(mapsnd_Batch ret ∘ binddt (batch (W * A) (T B))) t
    rewrite (kdtm_morph
               (Batch _ (T B))
               (Batch _ B)
               (ϕ := fun C => mapsnd_Batch (B1 := B) (B2 := T B) ret)
               (batch (W * A) (T B))).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
binddt (map ret ∘ batch (W * A) B) t =
binddt (mapsnd_Batch ret ∘ batch (W * A) (T B)) t
    reflexivity.
  Qed.

  Lemma toBatch6_toBatch7
    {A B: Type}:
    toBatch6 (A := A) (B := B) = mapfst_Batch extract ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
toBatch6 = mapfst_Batch extract ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
toBatch6 = mapfst_Batch extract ∘ toBatch7
    intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
toBatch6 = mapfst_Batch extract ∘ toBatch7
    rewrite toBatch6_to_bindt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
bindt (batch A (T B)) =
mapfst_Batch extract ∘ toBatch7
    rewrite bindt_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
binddt (batch A (T B) ∘ extract) =
mapfst_Batch extract ∘ toBatch7
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
binddt (batch A (T B) ∘ extract) =
mapfst_Batch extract ∘ binddt (batch (W * A) (T B))
    rewrite (kdtm_morph (Batch (W * A) (T B)) (Batch A (T B))
               (ϕ := fun C => mapfst_Batch extract)).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
binddt (batch A (T B) ∘ extract) =
binddt (mapfst_Batch extract ∘ batch (W * A) (T B))
    reflexivity.
  Qed.

  (** ** Specification for <<binddt>> via <<toBatch7>> *)
  (********************************************************************)
  Lemma binddt_through_toBatch7:
    forall (G: Type -> Type) `{Applicative G}
      (A B: Type) (f: W * A -> G (T B)),
      binddt (T := T) (U := U) f =
        map (F := G) (extract_Batch) ∘
          traverse (T := BATCH1 (T B) (U B)) f ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
forall (G : Type -> Type) (Map_G : Map G)
  (Pure_G : Pure G) (Mult_G : Mult G),
Applicative G ->
forall (A B : Type) (f : W * A -> G (T B)),
binddt f = map extract_Batch ∘ traverse f ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
forall (G : Type -> Type) (Map_G : Map G)
  (Pure_G : Pure G) (Mult_G : Mult G),
Applicative G ->
forall (A B : Type) (f : W * A -> G (T B)),
binddt f = map extract_Batch ∘ traverse f ∘ toBatch7
    intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = map extract_Batch ∘ traverse f ∘ toBatch7
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f =
map extract_Batch ∘ traverse f
∘ binddt (batch (W * A) (T B))
    rewrite <- runBatch_via_traverse.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = runBatch f ∘ binddt (batch (W * A) (T B))
    rewrite (kdtm_morph (Batch (W * A) (T B)) G
               (morph := ApplicativeMorphism_runBatch)).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = binddt (runBatch f ∘ batch (W * A) (T B))
    rewrite (runBatch_batch G).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = binddt f
    reflexivity.
  Qed.

  Lemma binddt_through_runBatch `{Applicative G} `(f: W * A -> G (T B)):
    binddt (U := U) f = runBatch f ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = runBatch f ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = runBatch f ∘ toBatch7
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = runBatch f ∘ binddt (batch (W * A) (T B))
    rewrite (kdtm_morph (Batch (W * A) (T B)) G
               (morph := ApplicativeMorphism_runBatch)).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = binddt (runBatch f ∘ batch (W * A) (T B))
    rewrite (runBatch_batch G).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G (T B)
binddt f = binddt f
    reflexivity.
  Qed.

  Lemma bindt_through_runBatch `{Applicative G} `(f: A -> G (T B)):
    bindt (U := U) f = runBatch (f ∘ extract) ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G (T B)
bindt f = runBatch (f ∘ extract) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G (T B)
bindt f = runBatch (f ∘ extract) ∘ toBatch7
    rewrite bindt_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G (T B)
binddt (f ∘ extract) =
runBatch (f ∘ extract) ∘ toBatch7
    rewrite binddt_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G (T B)
runBatch (f ∘ extract) ∘ toBatch7 =
runBatch (f ∘ extract) ∘ toBatch7
    reflexivity.
  Qed.

  Lemma bindd_through_runBatch `(f: W * A -> T B):
    bindd (U := U) f = runBatch (G := fun A => A) f ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> T B
bindd f = runBatch f ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> T B
bindd f = runBatch f ∘ toBatch7
    rewrite bindd_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> T B
binddt f = runBatch f ∘ toBatch7
    rewrite binddt_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> T B
runBatch f ∘ toBatch7 = runBatch f ∘ toBatch7
    reflexivity.
  Qed.

  Lemma traverse_through_runBatch `{Applicative G} `(f: A -> G B):
    traverse (T := U) f = runBatch (map ret ∘ f ∘ extract) ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G B
traverse f =
runBatch (map ret ∘ f ∘ extract) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G B
traverse f =
runBatch (map ret ∘ f ∘ extract) ∘ toBatch7
    rewrite traverse_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G B
binddt (map ret ∘ f ∘ extract) =
runBatch (map ret ∘ f ∘ extract) ∘ toBatch7
    rewrite binddt_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: A -> G B
runBatch (map ret ∘ f ∘ extract) ∘ toBatch7 =
runBatch (map ret ∘ f ∘ extract) ∘ toBatch7
    reflexivity.
  Qed.

  Corollary mapdt_through_runBatch `{Applicative G} `(f: W * A -> G B):
    mapdt (T := U) f = runBatch (G := G) (map ret ∘ f) ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G B
mapdt f = runBatch (map ret ∘ f) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G B
mapdt f = runBatch (map ret ∘ f) ∘ toBatch7
    rewrite mapdt_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G B
binddt (map ret ∘ f) =
runBatch (map ret ∘ f) ∘ toBatch7
    rewrite binddt_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
Map_G: Map G
Pure_G: Pure G
Mult_G: Mult G
H: Applicative G
A, B: Type
f: W * A -> G B
runBatch (map ret ∘ f) ∘ toBatch7 =
runBatch (map ret ∘ f) ∘ toBatch7
    reflexivity.
  Qed.

  Corollary mapd_through_runBatch `(f: W * A -> B):
    mapd (T := U) f =
      runBatch (G := fun A => A) (ret (T := T) ∘ f) ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> B
mapd f = runBatch (ret ∘ f) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> B
mapd f = runBatch (ret ∘ f) ∘ toBatch7
    rewrite mapd_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> B
binddt (ret ∘ f) = runBatch (ret ∘ f) ∘ toBatch7
    rewrite binddt_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: W * A -> B
runBatch (ret ∘ f) ∘ toBatch7 =
runBatch (ret ∘ f) ∘ toBatch7
    reflexivity.
  Qed.

  Corollary map_through_runBatch `(f: A -> B):
    map (F := U) f = runBatch (G := fun A => A)
                       (ret (T := T) ∘ f ∘ extract) ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: A -> B
map f = runBatch (ret ∘ f ∘ extract) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: A -> B
map f = runBatch (ret ∘ f ∘ extract) ∘ toBatch7
    rewrite map_to_traverse.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: A -> B
traverse f = runBatch (ret ∘ f ∘ extract) ∘ toBatch7
    rewrite traverse_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
f: A -> B
runBatch (map ret ∘ f ∘ extract) ∘ toBatch7 =
runBatch (ret ∘ f ∘ extract) ∘ toBatch7
    reflexivity.
  Qed.

  Corollary id_through_runBatch: forall (A: Type),
      id (A := U A) =
        runBatch (G := fun A => A) (ret (T := T) ∘ extract) ∘ toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
forall A : Type,
id = runBatch (ret ∘ extract) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
forall A : Type,
id = runBatch (ret ∘ extract) ∘ toBatch7
    intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A: Type
id = runBatch (ret ∘ extract) ∘ toBatch7
    rewrite <- (fun_map_id (F := U)).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A: Type
map id = runBatch (ret ∘ extract) ∘ toBatch7
    rewrite map_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A: Type
runBatch (ret ∘ id ∘ extract) ∘ toBatch7 =
runBatch (ret ∘ extract) ∘ toBatch7
    reflexivity.
  Qed.

  (** ** Naturality of <<toBatch7>> *)
  (********************************************************************)
  Lemma toBatch7_mapfst1
    `{Kleisli.DecoratedTraversableMonad.DecoratedTraversableMonad W T}
    {A A' B: Type} (f: W * A -> A'):
    toBatch7 ∘ mapd (T := T) f =
      mapfst_Batch (cobind f) ∘ toBatch7 (A := A) (B := B).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
op1: Monoid_op W
unit1: Monoid_unit W
Return_inst: Return T
Bindd_T_inst0: Binddt W T T
H: DecoratedTraversableMonad W T
A, A', B: Type
f: W * A -> A'
toBatch7 ∘ mapd f = mapfst_Batch (cobind f) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
op1: Monoid_op W
unit1: Monoid_unit W
Return_inst: Return T
Bindd_T_inst0: Binddt W T T
H: DecoratedTraversableMonad W T
A, A', B: Type
f: W * A -> A'
toBatch7 ∘ mapd f = mapfst_Batch (cobind f) ∘ toBatch7
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
op1: Monoid_op W
unit1: Monoid_unit W
Return_inst: Return T
Bindd_T_inst0: Binddt W T T
H: DecoratedTraversableMonad W T
A, A', B: Type
f: W * A -> A'
binddt (batch (W * A') (T B)) ∘ mapd f =
mapfst_Batch (cobind f) ∘ toBatch7
    rewrite (binddt_mapd).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
op1: Monoid_op W
unit1: Monoid_unit W
Return_inst: Return T
Bindd_T_inst0: Binddt W T T
H: DecoratedTraversableMonad W T
A, A', B: Type
f: W * A -> A'
binddt (kc1 (batch (W * A') (T B)) f) =
mapfst_Batch (cobind f) ∘ toBatch7
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
op1: Monoid_op W
unit1: Monoid_unit W
Return_inst: Return T
Bindd_T_inst0: Binddt W T T
H: DecoratedTraversableMonad W T
A, A', B: Type
f: W * A -> A'
binddt (kc1 (batch (W * A') (T B)) f) =
mapfst_Batch (cobind f) ∘ binddt (batch (W * A) (T B))
    rewrite
      (kdtm_morph (T := T) (U := T)
         (Batch (W * A) _)
         (Batch (W * A') _)
         (ϕ := fun A => mapfst_Batch (cobind f)) (batch (W * A) (T B))).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
op1: Monoid_op W
unit1: Monoid_unit W
Return_inst: Return T
Bindd_T_inst0: Binddt W T T
H: DecoratedTraversableMonad W T
A, A', B: Type
f: W * A -> A'
binddt (kc1 (batch (W * A') (T B)) f) =
binddt (mapfst_Batch (cobind f) ∘ batch (W * A) (T B))
    rewrite ret_natural.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
op1: Monoid_op W
unit1: Monoid_unit W
Return_inst: Return T
Bindd_T_inst0: Binddt W T T
H: DecoratedTraversableMonad W T
A, A', B: Type
f: W * A -> A'
binddt (kc1 (batch (W * A') (T B)) f) =
binddt (batch (W * A') (T B) ∘ cobind f)
    reflexivity.
  Qed.

  Lemma toBatch7_mapfst2
    {A A' B: Type} (f: A -> A') {C: Type}:
    toBatch7 ∘ map (F := T) f =
      mapfst_Batch (map f) ∘ toBatch7 (A := A) (B := B).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: A -> A'
C: Type
toBatch7 ∘ map f = mapfst_Batch (map f) ∘ toBatch7
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: A -> A'
C: Type
toBatch7 ∘ map f = mapfst_Batch (map f) ∘ toBatch7
    rewrite (map_to_cobind (W := prod W)).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: A -> A'
C: Type
toBatch7 ∘ map f =
mapfst_Batch (cobind (f ∘ extract)) ∘ toBatch7
    rewrite <- toBatch7_mapfst1.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: A -> A'
C: Type
toBatch7 ∘ map f = toBatch7 ∘ mapd (f ∘ extract)
    rewrite map_to_mapd.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: A -> A'
C: Type
toBatch7 ∘ mapd (f ∘ extract) =
toBatch7 ∘ mapd (f ∘ extract)
    reflexivity.
  Qed.

  Lemma toBatch7_mapfst3
    {A A' B: Type} (f: W * A -> A'):
    mapfst_Batch f ∘ toBatch7 (U := U) (A := A) (B := B) =
      toBatch6 ∘ mapd (T := U) f.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ toBatch7 = toBatch6 ∘ mapd f
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ toBatch7 = toBatch6 ∘ mapd f
    rewrite toBatch6_toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ toBatch7 =
mapfst_Batch extract ∘ toBatch7 ∘ mapd f
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ binddt (batch (W * A) (T B)) =
mapfst_Batch extract ∘ toBatch7 ∘ mapd f
    rewrite toBatch7_to_binddt.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ binddt (batch (W * A) (T B)) =
mapfst_Batch extract ∘ binddt (batch (W * A') (T B))
∘ mapd f
    reassociate ->.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ binddt (batch (W * A) (T B)) =
mapfst_Batch extract
∘ (binddt (batch (W * A') (T B)) ∘ mapd f)
    rewrite (binddt_mapd).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ binddt (batch (W * A) (T B)) =
mapfst_Batch extract
∘ binddt (kc1 (batch (W * A') (T B)) f)
    rewrite (kdtm_morph (T := T) (U := U)
               (Batch (W * A') _)
               (Batch A' _)
               (ϕ := fun A => mapfst_Batch extract)).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
mapfst_Batch f ∘ binddt (batch (W * A) (T B)) =
binddt
  (mapfst_Batch extract ∘ kc1 (batch (W * A') (T B)) f)
    rewrite (kdtm_morph (T := T) (U := U)
               (Batch (W * A) (T B))
               (Batch A' (T B))
               (ϕ := fun A => mapfst_Batch f)
               (batch (W * A) (T B))).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
binddt (mapfst_Batch f ∘ batch (W * A) (T B)) =
binddt
  (mapfst_Batch extract ∘ kc1 (batch (W * A') (T B)) f)
    rewrite ret_natural.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
binddt (batch A' (T B) ∘ f) =
binddt
  (mapfst_Batch extract ∘ kc1 (batch (W * A') (T B)) f)
    unfold kc1.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
binddt (batch A' (T B) ∘ f) =
binddt
  (mapfst_Batch extract
   ∘ (batch (W * A') (T B) ∘ cobind f))
    reassociate <- on right.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
binddt (batch A' (T B) ∘ f) =
binddt
  (mapfst_Batch extract ∘ batch (W * A') (T B)
   ∘ cobind f)
    rewrite ret_natural.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
binddt (batch A' (T B) ∘ f) =
binddt (batch A' (T B) ∘ extract ∘ cobind f)
    reassociate -> on right.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
binddt (batch A' (T B) ∘ f) =
binddt (batch A' (T B) ∘ (extract ∘ cobind f))
    rewrite kcom_cobind0.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, A', B: Type
f: W * A -> A'
binddt (batch A' (T B) ∘ f) =
binddt (batch A' (T B) ∘ f)
    reflexivity.
  Qed.

  (** ** Respectfulness for <<binddt>> *)
  (********************************************************************)
  Lemma binddt_respectful_core
    {G} `{Mult G} `{Map G} `{Pure G}:
    forall (A B: Type) (t: U A) (f g: W * A -> G (T B)),
      (forall (w: W) (a: A), (w, a) ∈d t -> f (w, a) = g (w, a)) =
        Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
forall (A B : Type) (t : U A) (f g : W * A -> G (T B)),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) =
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
forall (A B : Type) (t : U A) (f g : W * A -> G (T B)),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) =
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t
    intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
A, B: Type
t: U A
f, g: W * A -> G (T B)
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) =
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t
    apply propositional_extensionality.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
A, B: Type
t: U A
f, g: W * A -> G (T B)
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) <->
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t
    rewrite forall_ctx_iff.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
A, B: Type
t: U A
f, g: W * A -> G (T B)
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) <->
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a))
    reflexivity.
  Qed.

  Theorem binddt_respectful
    {G} `{Mult G} `{Map G} `{Pure G} `{! Applicative G}:
    forall (A B: Type) (t: U A)
      (f g: W * A -> G (T B)),
      (forall (w: W) (a: A), (w, a) ∈d t -> f (w, a) = g (w, a))
      -> binddt f t = binddt (U := U) g t.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
forall (A B : Type) (t : U A) (f g : W * A -> G (T B)),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) ->
binddt f t = binddt g t
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
forall (A B : Type) (t : U A) (f g : W * A -> G (T B)),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) ->
binddt f t = binddt g t
    introv.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) ->
binddt f t = binddt g t
    rewrite (binddt_respectful_core).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t ->
binddt f t = binddt g t
    unfold Forall_ctx.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
mapdReduce (fun '(w, a) => f (w, a) = g (w, a)) t ->
binddt f t = binddt g t
    rewrite (mapdReduce_through_runBatch2 A B).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
(runBatch (fun '(w, a) => f (w, a) = g (w, a))
 ∘ toBatch3) t -> binddt f t = binddt g t
    do 2 rewrite binddt_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
(runBatch (fun '(w, a) => f (w, a) = g (w, a))
 ∘ toBatch3) t ->
(runBatch f ∘ toBatch7) t = (runBatch g ∘ toBatch7) t
    unfold compose.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
runBatch (fun '(w, a) => f (w, a) = g (w, a))
  (toBatch3 t) ->
runBatch f (toBatch7 t) = runBatch g (toBatch7 t)
    rewrite toBatch3_to_toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
runBatch (fun '(w, a) => f (w, a) = g (w, a))
  (mapsnd_Batch ret (toBatch7 t)) ->
runBatch f (toBatch7 t) = runBatch g (toBatch7 t)
    rewrite <- runBatch_mapsnd.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (toBatch7 t) ->
runBatch f (toBatch7 t) = runBatch g (toBatch7 t)
    induction (toBatch7 t).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
c: C
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (Done c) ->
runBatch f (Done c) = runBatch g (Done c)
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
b: Batch (W * A) (T B) (T B -> C)
a: W * A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (b ⧆ a) -> runBatch f (b ⧆ a) = runBatch g (b ⧆ a)
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
c: C
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (Done c) ->
runBatch f (Done c) = runBatch g (Done c) cbn.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
c: C
pure c -> pure c = pure c reflexivity.
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
b: Batch (W * A) (T B) (T B -> C)
a: W * A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (b ⧆ a) -> runBatch f (b ⧆ a) = runBatch g (b ⧆ a) destruct a as [w a].
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (b ⧆ (w, a)) ->
runBatch f (b ⧆ (w, a)) = runBatch g (b ⧆ (w, a))
      cbn.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a))) b
● (f (w, a) = g (w, a)) ->
ap G (runBatch f b) (f (w, a)) =
ap G (runBatch g b) (g (w, a))
      intros [hyp1 hyp2].
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
hyp1: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b
hyp2: f (w, a) = g (w, a)
ap G (runBatch f b) (f (w, a)) =
ap G (runBatch g b) (g (w, a))
      rewrite hyp2.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A, B: Type
t: U A
f, g: W * A -> G (T B)
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
hyp1: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b
hyp2: f (w, a) = g (w, a)
ap G (runBatch f b) (g (w, a)) =
ap G (runBatch g b) (g (w, a))
      rewrite IHb; auto.
  Qed.

  Theorem binddt_respectful_pure
    {G} `{Mult G} `{Map G} `{Pure G} `{! Applicative G}:
    forall (A: Type) (t: U A)
      (f: W * A -> G (T A)),
      (forall (w: W) (a: A),
          (w, a) ∈d t ->
          f (w, a) = pure (F := G) (ret (T := T) a))
      -> binddt f t = pure t.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
forall (A : Type) (t : U A) (f : W * A -> G (T A)),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = pure (ret a)) ->
binddt f t = pure t
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
forall (A : Type) (t : U A) (f : W * A -> G (T A)),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = pure (ret a)) ->
binddt f t = pure t
    intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A: Type
t: U A
f: W * A -> G (T A)
H2: forall (w : W) (a : A),
(w, a) ∈d t -> f (w, a) = pure (ret a)
binddt f t = pure t
    rewrite <- (binddt_pure A).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
G: Type -> Type
H: Mult G
H0: Map G
H1: Pure G
Applicative0: Applicative G
A: Type
t: U A
f: W * A -> G (T A)
H2: forall (w : W) (a : A),
(w, a) ∈d t -> f (w, a) = pure (ret a)
binddt f t = binddt (pure ∘ ret ∘ extract) t
    apply binddt_respectful;
    assumption.
  Qed.

  (** ** Respectfulness for <<bindd>> *)
  (********************************************************************)
  Lemma bindd_respectful_core:
    forall (A B: Type) (t: U A) (f g: W * A -> T B),
      (forall (w: W) (a: A), (w, a) ∈d t -> f (w, a) = g (w, a)) =
        Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
forall (A B : Type) (t : U A) (f g : W * A -> T B),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) =
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t
    intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) =
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t
    apply propositional_extensionality.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) <->
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t
    rewrite forall_ctx_iff.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) <->
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a))
    reflexivity.
  Qed.

  Theorem bindd_respectful:
    forall (A B: Type) (t: U A) (f g: W * A -> T B),
      (forall (w: W) (a: A), (w, a) ∈d t -> f (w, a) = g (w, a))
      -> bindd f t = bindd (U := U) g t.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
forall (A B : Type) (t : U A) (f g : W * A -> T B),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) ->
bindd f t = bindd g t
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
forall (A B : Type) (t : U A) (f g : W * A -> T B),
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) ->
bindd f t = bindd g t
    introv.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
(forall (w : W) (a : A),
 (w, a) ∈d t -> f (w, a) = g (w, a)) ->
bindd f t = bindd g t
    rewrite (bindd_respectful_core A B t f g).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
Forall_ctx (fun '(w, a) => f (w, a) = g (w, a)) t ->
bindd f t = bindd g t
    unfold Forall_ctx.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
mapdReduce (fun '(w, a) => f (w, a) = g (w, a)) t ->
bindd f t = bindd g t
    rewrite (mapdReduce_through_runBatch2 A B).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
(runBatch (fun '(w, a) => f (w, a) = g (w, a))
 ∘ toBatch3) t -> bindd f t = bindd g t
    do 2 rewrite bindd_through_runBatch.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
(runBatch (fun '(w, a) => f (w, a) = g (w, a))
 ∘ toBatch3) t ->
(runBatch f ∘ toBatch7) t = (runBatch g ∘ toBatch7) t
    unfold compose.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
runBatch (fun '(w, a) => f (w, a) = g (w, a))
  (toBatch3 t) ->
runBatch f (toBatch7 t) = runBatch g (toBatch7 t)
    rewrite toBatch3_to_toBatch7.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
runBatch (fun '(w, a) => f (w, a) = g (w, a))
  (mapsnd_Batch ret (toBatch7 t)) ->
runBatch f (toBatch7 t) = runBatch g (toBatch7 t)
    rewrite <- runBatch_mapsnd.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (toBatch7 t) ->
runBatch f (toBatch7 t) = runBatch g (toBatch7 t)
    induction (toBatch7 t).
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
c: C
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (Done c) ->
runBatch f (Done c) = runBatch g (Done c)
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
b: Batch (W * A) (T B) (T B -> C)
a: W * A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (b ⧆ a) -> runBatch f (b ⧆ a) = runBatch g (b ⧆ a)
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
c: C
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (Done c) ->
runBatch f (Done c) = runBatch g (Done c) cbn.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
c: C
pure c -> pure c = pure c reflexivity.
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
b: Batch (W * A) (T B) (T B -> C)
a: W * A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (b ⧆ a) -> runBatch f (b ⧆ a) = runBatch g (b ⧆ a) destruct a as [w a].
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a)))
  (b ⧆ (w, a)) ->
runBatch f (b ⧆ (w, a)) = runBatch g (b ⧆ (w, a))
      cbn.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
runBatch
  (map ret ∘ (fun '(w, a) => f (w, a) = g (w, a))) b
● (f (w, a) = g (w, a)) ->
runBatch f b (f (w, a)) = runBatch g b (g (w, a))
      intros [hyp1 hyp2].
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
hyp1: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b
hyp2: f (w, a) = g (w, a)
runBatch f b (f (w, a)) = runBatch g b (g (w, a))
      rewrite hyp2.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ToBatch7_WTT: ToBatch7 W T T
ToBatch7_WTU: ToBatch7 W T U
Compat_ToBatch7_Binddt0: Compat_ToBatch7_Binddt W T T
Compat_ToBatch7_Binddt1: Compat_ToBatch7_Binddt W T U
ToSubset_U_inst: ToSubset U
ToSubset_T_inst: ToSubset T
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
ToBatch3_TU: ToBatch3 W U
Compat_ToBatch3_Mapdt0: Compat_ToBatch3_Mapdt W U
ToBatch6_TU: ToBatch6 T U
Compat_ToBatch6_Bindt0: Compat_ToBatch6_Bindt T U
A, B: Type
t: U A
f, g: W * A -> T B
C: Type
b: Batch (W * A) (T B) (T B -> C)
w: W
a: A
IHb: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b ->
runBatch f b = runBatch g b
hyp1: runBatch
  (map ret
   ∘ (fun '(w, a) => f (w, a) = g (w, a))) b
hyp2: f (w, a) = g (w, a)
runBatch f b (g (w, a)) = runBatch g b (g (w, a))
      rewrite IHb; auto.
  Qed.

End decorated_traversable_monad_theory.

Section instances.

  Context
    `{op: Monoid_op W}
    `{unit: Monoid_unit W}
    `{Monoid_inst: Monoid W}.

  Context
    `{ret_inst: Return T}
    `{Map_T_inst: Map T}
    `{Mapd_T_inst: Mapd W T}
    `{Traverse_T_inst: Traverse T}
    `{Bind_T_inst: Bind T T}
    `{Mapdt_T_inst: Mapdt W T}
    `{Bindd_T_inst: Bindd W T T}
    `{Bindt_T_inst: Bindt T T}
    `{Binddt_T_inst: Binddt W T T}
    `{ToSubset_T_inst: ToSubset T}
    `{! Compat_Map_Binddt W T T}
    `{! Compat_Mapd_Binddt W T T}
    `{! Compat_Traverse_Binddt W T T}
    `{! Compat_Bind_Binddt W T T}
    `{! Compat_Mapdt_Binddt W T T}
    `{! Compat_Bindd_Binddt W T T}
    `{! Compat_Bindt_Binddt W T T}.

  Context
    `{Map_U_inst: Map U}
    `{Mapd_U_inst: Mapd W U}
    `{Traverse_U_inst: Traverse U}
    `{Bind_U_inst: Bind T U}
    `{Mapdt_U_inst: Mapdt W U}
    `{Bindd_U_inst: Bindd W T U}
    `{Bindt_U_inst: Bindt T U}
    `{Binddt_U_inst: Binddt W T U}
    `{ToSubset_U_inst: ToSubset U}
    `{! Compat_Map_Binddt W T U}
    `{! Compat_Mapd_Binddt W T U}
    `{! Compat_Traverse_Binddt W T U}
    `{! Compat_Bind_Binddt W T U}
    `{! Compat_Mapdt_Binddt W T U}
    `{! Compat_Bindd_Binddt W T U}
    `{! Compat_Bindt_Binddt W T U}
    `{! Compat_ToSubset_Traverse T}
    `{! Compat_ToSubset_Traverse U}.

  Context
    `{ToCtxset_T_inst: ToCtxset W T}
    `{ToCtxset_U_inst: ToCtxset W U}
    `{! Compat_ToCtxset_Mapdt W T}
    `{! Compat_ToCtxset_Mapdt W U}.

  Context
    `{ToCtxlist_T_inst: ToCtxlist W T}
    `{ToCtxlist_U_inst: ToCtxlist W U}
    `{! Compat_ToCtxlist_Mapdt W T}
    `{! Compat_ToCtxlist_Mapdt W U}.

  Context
    `{Monad_inst: ! DecoratedTraversableMonad W T}
    `{Module_inst: ! DecoratedTraversableRightPreModule W T U}.

  Import
    Kleisli.TraversableMonad.DerivedInstances
    Kleisli.DecoratedTraversableMonad.DerivedInstances
    KleisliToCoalgebraic.TraversableMonad.DerivedOperations
    KleisliToCoalgebraic.DecoratedTraversableFunctor.DerivedOperations
    KleisliToCoalgebraic.DecoratedTraversableMonad.DerivedOperations.

  #[export] Instance DecoratedContainerFunctor_DTM:
    DecoratedContainerFunctor W U.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedContainerFunctor W U
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedContainerFunctor W U
    constructor.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedFunctor W U
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedHom W U (ctxset W)
  (@toctxset W U ToCtxset_U_inst)
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
forall (A B : Type) (t : U A) (f g : W * A -> B),
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a)) ->
mapd f t = mapd g t
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedFunctor W U typeclasses eauto.
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedHom W U (ctxset W)
  (@toctxset W U ToCtxset_U_inst) typeclasses eauto.
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
forall (A B : Type) (t : U A) (f g : W * A -> B),
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a)) ->
mapd f t = mapd g t intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
A, B: Type
t: U A
f, g: W * A -> B
H: forall (e : W) (a : A),
(e, a) ∈d t -> f (e, a) = g (e, a)
mapd f t = mapd g t
      apply mapd_respectful.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
A, B: Type
t: U A
f, g: W * A -> B
H: forall (e : W) (a : A),
(e, a) ∈d t -> f (e, a) = g (e, a)
forall (e : W) (a : A),
(e, a) ∈d t -> f (e, a) = g (e, a)
      auto.
  Qed.

  #[export] Instance DecoratedContainerMonad_DTM:
    DecoratedContainerMonad W T.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedContainerMonad W T
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedContainerMonad W T
    constructor.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedMonad W T
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedMonadHom W T (ctxset W)
  (@toctxset W T ToCtxset_T_inst)
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
forall (A B : Type) (t : T A) (f g : W * A -> T B),
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a)) ->
bindd f t = bindd g t
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedMonad W T typeclasses eauto.
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedMonadHom W T (ctxset W)
  (@toctxset W T ToCtxset_T_inst) typeclasses eauto.
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
forall (A B : Type) (t : T A) (f g : W * A -> T B),
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a)) ->
bindd f t = bindd g t intros.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
A, B: Type
t: T A
f, g: W * A -> T B
H: forall (e : W) (a : A),
(e, a) ∈d t -> f (e, a) = g (e, a)
bindd f t = bindd g t
      apply bindd_respectful.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
A, B: Type
t: T A
f, g: W * A -> T B
H: forall (e : W) (a : A),
(e, a) ∈d t -> f (e, a) = g (e, a)
forall (w : W) (a : A),
(w, a) ∈d t -> f (w, a) = g (w, a)
      auto.
  Qed.

  #[export] Instance DecoratedContainerModule_DTM:
    DecoratedContainerRightModule W T U.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedContainerRightModule W T U
  Proof.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedContainerRightModule W T U
    constructor.
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedRightModule W T U
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ParallelDecoratedRightModuleHom T 
  (ctxset W) U (ctxset W)
  (@toctxset W T ToCtxset_T_inst)
  (@toctxset W U ToCtxset_U_inst)
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
forall (A B : Type) (t : U A) (f g : W * A -> T B),
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a)) ->
bindd f t = bindd g t
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
DecoratedRightModule W T U apply (DecoratedRightModule_DecoratedTraversableRightPreModule W T U).
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
ParallelDecoratedRightModuleHom T (ctxset W) U
  (ctxset W) (@toctxset W T ToCtxset_T_inst)
  (@toctxset W U ToCtxset_U_inst) typeclasses eauto.
    -
W: Type
op: Monoid_op W
unit: Monoid_unit W
op0: Monoid_op W
unit0: Monoid_unit W
Monoid_inst: Monoid W
T: Type -> Type
ret_inst: Return T
Map_T_inst: Map T
Mapd_T_inst: Mapd W T
Traverse_T_inst: Traverse T
Bind_T_inst: Bind T T
Mapdt_T_inst: Mapdt W T
Bindd_T_inst: Bindd W T T
Bindt_T_inst: Bindt T T
Binddt_T_inst: Binddt W T T
ToSubset_T_inst: ToSubset T
Compat_Map_Binddt0: Compat_Map_Binddt W T T
Compat_Mapd_Binddt0: Compat_Mapd_Binddt W T T
Compat_Traverse_Binddt0: Compat_Traverse_Binddt W T T
Compat_Bind_Binddt0: Compat_Bind_Binddt W T T
Compat_Mapdt_Binddt0: Compat_Mapdt_Binddt W T T
Compat_Bindd_Binddt0: Compat_Bindd_Binddt W T T
Compat_Bindt_Binddt0: Compat_Bindt_Binddt W T T
U: Type -> Type
Map_U_inst: Map U
Mapd_U_inst: Mapd W U
Traverse_U_inst: Traverse U
Bind_U_inst: Bind T U
Mapdt_U_inst: Mapdt W U
Bindd_U_inst: Bindd W T U
Bindt_U_inst: Bindt T U
Binddt_U_inst: Binddt W T U
ToSubset_U_inst: ToSubset U
Compat_Map_Binddt1: Compat_Map_Binddt W T U
Compat_Mapd_Binddt1: Compat_Mapd_Binddt W T U
Compat_Traverse_Binddt1: Compat_Traverse_Binddt W T U
Compat_Bind_Binddt1: Compat_Bind_Binddt W T U
Compat_Mapdt_Binddt1: Compat_Mapdt_Binddt W T U
Compat_Bindd_Binddt1: Compat_Bindd_Binddt W T U
Compat_Bindt_Binddt1: Compat_Bindt_Binddt W T U
Compat_ToSubset_Traverse0: Compat_ToSubset_Traverse T
Compat_ToSubset_Traverse1: Compat_ToSubset_Traverse U
ToCtxset_T_inst: ToCtxset W T
ToCtxset_U_inst: ToCtxset W U
Compat_ToCtxset_Mapdt0: Compat_ToCtxset_Mapdt W T
Compat_ToCtxset_Mapdt1: Compat_ToCtxset_Mapdt W U
ToCtxlist_T_inst: ToCtxlist W T
ToCtxlist_U_inst: ToCtxlist W U
Compat_ToCtxlist_Mapdt0: Compat_ToCtxlist_Mapdt W T
Compat_ToCtxlist_Mapdt1: Compat_ToCtxlist_Mapdt W U
Monad_inst: DecoratedTraversableMonad W T
Module_inst: DecoratedTraversableRightPreModule W T U
forall (A B : Type) (t : U A) (f g : W * A -> T B),
(forall (e : W) (a : A),
 (e, a) ∈d t -> f (e, a) = g (e, a)) ->
bindd f t = bindd g t intros; apply bindd_respectful; auto.
  Qed.

End instances.

(** * Deriving All Other Typeclass Instances from a DTM *)
(**********************************************************************)
Module UsefulInstances.

  Export Classes.Coalgebraic.TraversableFunctor.
  Export Classes.Coalgebraic.TraversableMonad.
  Export Classes.Coalgebraic.DecoratedTraversableFunctor.
  Export Classes.Coalgebraic.DecoratedTraversableMonad.

  Export Classes.Kleisli.TraversableFunctor.
  Export Classes.Kleisli.TraversableMonad.
  Export Classes.Kleisli.DecoratedTraversableFunctor.
  Export Classes.Kleisli.DecoratedTraversableMonad.


  Export KleisliToCoalgebraic.TraversableFunctor.
  Export KleisliToCoalgebraic.TraversableFunctor.DerivedOperations.
  Export KleisliToCoalgebraic.TraversableFunctor.DerivedInstances.

  Export KleisliToCoalgebraic.TraversableMonad.
  Export KleisliToCoalgebraic.TraversableMonad.DerivedOperations.
  Export KleisliToCoalgebraic.TraversableMonad.DerivedInstances.

  Export KleisliToCoalgebraic.DecoratedTraversableFunctor.
  Export KleisliToCoalgebraic.DecoratedTraversableFunctor.DerivedOperations.
  Export KleisliToCoalgebraic.DecoratedTraversableFunctor.DerivedInstances.

  Export KleisliToCoalgebraic.DecoratedTraversableMonad.
  Export KleisliToCoalgebraic.DecoratedTraversableMonad.DerivedOperations.
  Export KleisliToCoalgebraic.DecoratedTraversableMonad.DerivedInstances.

  (*
  Export Kleisli.DecoratedTraversableFunctor.DerivedOperations.
  Export Kleisli.DecoratedTraversableFunctor.DerivedInstances.
   *)

  Export Kleisli.DecoratedTraversableMonad.DerivedOperations.
  Export Kleisli.DecoratedTraversableMonad.DerivedInstances.

  #[export] Existing Instance Tolist_Traverse.
  #[export] Existing Instance ToSubset_Traverse.
  #[export] Existing Instance ToCtxlist_Mapdt.
  #[export] Existing Instance ToCtxset_Mapdt.

End UsefulInstances.