Imported Upstream version 8.6upstream/8.6

1 files changed, 35 insertions, 0 deletions

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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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