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Require Import Coq.Setoids.Setoid Coq.Classes.Morphisms.
Definition f (v : option nat) := match v with
| Some k => Some k
| None => None
end.
Axioms F G : (option nat -> option nat) -> Prop.
Axiom FG : forall f, f None = None -> F f = G f.
Axiom admit : forall {T}, T.
Existing Instance eq_Reflexive.
Global Instance foo (A := nat)
: Proper ((pointwise_relation _ eq)
==> eq ==> forall_relation (fun _ => Basics.flip Basics.impl))
(@option_rect A (fun _ => Prop)) | 0.
exact admit.
Qed.
Global Instance bar (A := nat)
: Proper ((pointwise_relation _ eq)
==> eq ==> eq ==> Basics.flip Basics.impl)
(@option_rect A (fun _ => Prop)) | 0.
exact admit.
Qed.
Goal forall k, option_rect (fun _ => Prop) (fun v : nat => v = v /\ F f) True k.
Proof.
intro.
pose proof (_ : (Proper (_ ==> eq ==> _) and)).
setoid_rewrite (FG _ _); [ | reflexivity.. ].
Undo.
setoid_rewrite (FG _ eq_refl). (* Error: Tactic failure: setoid rewrite failed: Nothing to rewrite. in 8.5 *) Admitted.
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