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+Require Import Coq.Classes.Morphisms Coq.Classes.RelationClasses Coq.Program.Program Coq.Setoids.Setoid.
+
+Global Set Implicit Arguments.
+
+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' _ _ _).