proposition: Lemma ordinal_in_universe a: ordinalp a -> sub a (universe a).
proof: Proof. move => oa; case: (least_ordinal6 (fun z => sub z (universe z)) oa) => //. set z := least_ordinal _ _; move => [oz h]; case. move => t tz; move: (h _ tz) => /setP_P. have ot:= (Os_ordinal oz tz). have: osucc t <=o z by apply /oleSltP; apply/(oltP oz). rewrite - (universe_succ ot) => /universe_inc2; apply. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)