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+Module File1.
+ Module Export DirA.
+ Module A.
+ Inductive paths {A : Type} (a : A) : A -> Type :=
+ idpath : paths a a.
+
+ Arguments idpath {A a} , [A] a.
+
+ Notation "x = y :> A" := (@paths A x y) : type_scope.
+ Notation "x = y" := (x = y :>_) : type_scope.
+ End A.
+ End DirA.
+End File1.
+
+Module File2.
+ Module Export DirA.
+ Module B.
+ Import File1.
+ Export A.
+ Lemma foo : forall x y : Type, x = y -> y = x.
+ Proof.
+ intros x y H.
+ rewrite <- H.
+ constructor.
+ Qed.
+ End B.
+ End DirA.
+End File2.
+
+Module File3.
+ Module Export DirA.
+ Module C.
+ Import File1.
+ Export A.
+ Lemma bar : forall x y : Type, x = y -> y = x.
+ Proof.
+ intros x y H.
+ rewrite <- H.
+ constructor.
+ Defined.
+ Definition bar'
+ := Eval cbv beta iota zeta delta [bar internal_paths_rew] in bar.
+ End C.
+ End DirA.
+End File3.