proposition: Lemma pfwdef : forall S (F : PartFunct S) x y Hx Hy, x [=] y -> F x Hx [=] F y Hy.
proof: Proof. intros. apply not_ap_imp_eq; intro H0. generalize (pfstrx _ _ _ _ _ _ H0). exact (eq_imp_not_ap _ _ _ H). Qed.
imports: CoRN.algebra.CSetoids