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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.
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