proposition: Lemma not_ap_imp_eq : forall x y : S, Not (x [#] y) -> x [=] y.
proof: Proof. intros x y. elim (ap_tight S x y). intros H1 H2. assumption. Qed.
imports: CoRN.tactics.CornTac CoRN.logic.CLogic CoRN.tactics.Step CoRN.algebra.RSetoid