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Require Import TestSuite.admit.
From Stdlib Require Import Morphisms RelationClasses Program Setoid.
Global Set Implicit Arguments.
#[export] Hint Extern 0 => apply reflexivity : typeclass_instances.
Inductive Comp : Type -> Type :=
| Pick : forall A, (A -> Prop) -> Comp A.
Axiom computes_to : forall A, Comp A -> A -> Prop.
Axiom refine : forall {A} (old : Comp A) (new : Comp A), Prop.
Global Instance refine_PreOrder A : PreOrder (@refine A).
Admitted.
Add Parametric Morphism A
: (@Pick A)
with signature
(pointwise_relation _ (flip impl))
==> (@refine A)
as refine_flip_impl_Pick.
admit.
Defined.
Definition remove_forall_eq' A x B (P : A -> B -> Prop) : pointwise_relation _ impl (P x) (fun z => forall y : A, y = x -> P y z).
admit.
Defined.
Goal forall A B (x : A) (P : _ -> _ -> Prop),
refine (Pick (fun n : B => forall y, y = x -> P y n))
(Pick (fun n : B => P x n)).
Proof.
intros.
setoid_rewrite (@remove_forall_eq' _ _ _ _).
Undo.
(* This failed with NotConvertible at some time *)
setoid_rewrite (@remove_forall_eq' _ _ _).
Abort.
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