proposition: Lemma all_equiv2_impl__stronger : forall l1 l2 x y, all_equiv l1 -> all_equiv l2 -> In x l1 -> In y l2 -> (x -> y) -> stronger l1 l2.
proof: Proof. intros l1 l2 x y Heq1 Heq2 HxIn HyIn Hxy x1 y1 Hx1In Hy1In. rewrite (Heq1 x1 x); [rewrite (Heq2 y1 y)|..]; assumption. Qed.
imports: List