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+
+Module X.
+ (*Set Universe Polymorphism.*)
+ Inductive paths A (x : A) : forall _ : A, Type := idpath : paths A x x.
+ Notation "x = y" := (@paths _ x y) (at level 70, no associativity) : type_scope.
+
+ Axioms A B : Type.
+ Axiom P : A = B.
+ Definition foo : A = B.
+ abstract (rewrite <- P; reflexivity).
+ Defined.
+End X.
+
+Module Y.
+ (*Set Universe Polymorphism.*)
+ Inductive paths A (x : A) : forall _ : A, Type := idpath : paths A x x.
+ Notation "x = y" := (@paths _ x y) (at level 70, no associativity) : type_scope.
+
+ Axioms A B : Type.
+ Axiom P : A = B.
+ Definition foo : (A = B) * (A = B).
+ split; abstract (rewrite <- P; reflexivity).
+ Defined.
+End Y.