proposition: Theorem lt_diff : forall a b:A, lt a b -> a <> b.
proof: Proof. induction a as [| x l IHl]; destruct b; cbn. - contradiction. - discriminate. - contradiction. - intros [H | [H1 H2]]. + intro e; injection e; intros; subst x; apply (M.lt_irreflexive a); auto. + intro e; injection e; intros; subst a b; now apply (IHl l). Qed.
imports: DecOrders