proposition: Lemma nsv_Sn a b: ordinalp a -> ordinalp b -> S (osucc a) b = osucc (S a b).
proof: Proof. move => oa; move:b; apply: least_ordinal2 => b ob bp. apply: oleA; last by apply /oleSltP; exact: (nsv_ltl (oltS oa) ob). apply: (nsv_le_prop (OS_succ oa) ob (OS_succ (OS_nsv oa ob))) => x. by move/oltSleP => sxa; apply/oltSleP; apply:nsv_lel. by move => xb; rewrite (bp _ xb); apply/oltSSP; apply:nsv_ltr. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)