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+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+
+
+Require Import Setoid.
+Set Primitive Projections.
+
+
+Module CoqBug.
+Record foo A := Foo { foo_car : A }.
+
+Definition bar : foo _ := Foo nat 10.
+
+Variable alias : forall A, foo A -> A.
+
+Parameter e : @foo_car = alias.
+
+Goal foo_car _ bar = alias _ bar.
+Proof.
+(* Coq equally fails *)
+Fail rewrite -> e.
+Fail rewrite e at 1.
+Fail setoid_rewrite e.
+Fail setoid_rewrite e at 1.
+Set Keyed Unification.
+Fail rewrite -> e.
+Fail rewrite e at 1.
+Fail setoid_rewrite e.
+Fail setoid_rewrite e at 1.
+Admitted.
+
+End CoqBug.
+
+(* ----------------------------------------------- *)
+Require Import ssreflect.
+
+Set Primitive Projections.
+
+Module T1.
+
+Record foo A := Foo { foo_car : A }.
+
+Definition bar : foo _ := Foo nat 10.
+
+Goal foo_car _ bar = 10.
+Proof.
+match goal with
+| |- foo_car _ bar = 10 => idtac
+end.
+rewrite /foo_car.
+(*
+Fail match goal with
+| |- foo_car _ bar = 10 => idtac
+end.
+*)
+Admitted.
+
+End T1.
+
+
+Module T2.
+
+Record foo {A} := Foo { foo_car : A }.
+
+Definition bar : foo := Foo nat 10.
+
+Goal foo_car bar = 10.
+match goal with
+| |- foo_car bar = 10 => idtac
+end.
+rewrite /foo_car.
+(*
+Fail match goal with
+| |- foo_car bar = 10 => idtac
+end.
+*)
+Admitted.
+
+End T2.
+
+
+Module T3.
+
+Record foo {A} := Foo { foo_car : A }.
+
+Definition bar : foo := Foo nat 10.
+
+Goal foo_car bar = 10.
+Proof.
+rewrite -[foo_car _]/(id _).
+match goal with |- id _ = 10 => idtac end.
+Admitted.
+
+Goal foo_car bar = 10.
+Proof.
+set x := foo_car _.
+match goal with |- x = 10 => idtac end.
+Admitted.
+
+End T3.
+
+Module T4.
+
+Inductive seal {A} (f : A) := { unseal : A; seal_eq : unseal = f }.
+Arguments unseal {_ _} _.
+Arguments seal_eq {_ _} _.
+
+Record uPred : Type := IProp { uPred_holds :> Prop }.
+
+Definition uPred_or_def (P Q : uPred) : uPred :=
+  {| uPred_holds := P \/ Q |}.
+Definition uPred_or_aux : seal (@uPred_or_def). by eexists. Qed.
+Definition uPred_or := unseal uPred_or_aux.
+Definition uPred_or_eq: @uPred_or = @uPred_or_def := seal_eq uPred_or_aux.
+
+Lemma foobar (P1 P2 Q : uPred) :
+  (P1 <-> P2) -> (uPred_or P1 Q) <-> (uPred_or P2 Q).
+Proof.
+  rewrite uPred_or_eq. (* This fails. *)
+Admitted.
+
+End T4.
+
+
+Module DesignFlaw.
+
+Record foo A := Foo { foo_car : A }.
+Definition bar : foo _ := Foo nat 10.
+
+Definition app (f : foo nat -> nat) x := f x.
+
+Goal app (foo_car _) bar = 10.
+Proof.
+unfold app.  (* mkApp should produce a Proj *)
+Fail set x := (foo_car _ _).
+Admitted.
+
+End DesignFlaw.
+
+
+Module Bug.
+
+Record foo A := Foo { foo_car : A }.
+
+Definition bar : foo _ := Foo nat 10.
+
+Variable alias : forall A, foo A -> A.
+
+Parameter e : @foo_car = alias.
+
+Goal foo_car _ bar = alias _ bar.
+Proof.
+Fail rewrite e.  (* Issue: #86 *)
+Admitted.
+
+End Bug.