proposition: Lemma nsv_ltl a1 a2 b: a1 <o a2 -> ordinalp b -> (S a1 b) <o (S a2 b).
proof: Proof. move => la1a2 ob; move: (proj32_1 la1a2) => oa2. rewrite (nsv_rec oa2 ob); apply:osup_ub. move => t /doubleI_rgP [][y yi ->]; apply:OS_nsv => //. apply: (Os_ordinal ob yi). apply: (Os_ordinal oa2 yi). by apply/doubleI_rgP; right; exists a1 => //; apply:olt_i. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)