proposition: Lemma osum_int_omega n: n <o omega0 -> n +o omega0 = omega0.
proof: Proof. move => no; move: (no) => [[on oo son] _]. set_extens t; last by apply: (proj33 (osum_M0le on oo)). rewrite (osum_rec_def on oo); case /setU2_P; first by apply: son. move => /funI_P [z zo ->]; apply /(oltP oo) /(osum2_lt_omega no). by apply/(oltP oo). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)