proposition: Lemma strict_sub_trans1 : forall a b c : E, strict_sub a b -> sub b c -> strict_sub a c.
proof: Proof. unfold strict_sub in |- *. unfold neq in |- *. unfold not in |- *. ir. xd. ir. ap H. ap extensionality. am. rewrite H2. am. xd. apply sub_trans with b; au. Qed.
imports: tactics