proposition: Lemma finite_sP x: finite_o (osucc x) <-> finite_o x.
proof: Proof. split; move => [p1 p2]. have ox := (OS_succr p1). by move: p2 => /(infinite_sP ox) h. by split; [ apply: OS_succ | move/(infinite_sP p1)]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)