proposition: Lemma all_equiv_chara : forall l, all_equiv l <-> forall x y, In x l -> In y l -> x -> y.
proof: Proof. unfold all_equiv. intro l; split. intros He x y Hx Hy; rewrite (He x y); auto. intros Himp x y Hxl Hyl. split; apply Himp; assumption. Qed.
imports: List