proposition: Lemma universe_inc2 a b: a <=o b -> sub (universe a) (universe b).
proof: Proof. move => lab. case: (equal_or_not a b); first by move => ->; fprops. move=> anb; move: (universe_inc1 (conj lab anb)). by apply: sub_trans => t ta; apply /setP_P; apply:(universe_trans (proj31 lab)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)