proposition: Lemma aleph_le_leo x y: x <=o y -> \omega x <=o \omega y.
proof: Proof. move => xy; case: (equal_or_not x y) => nxy. rewrite - nxy; exact: (oleR(OS_aleph (proj31 xy))). by move: (aleph_lt_lto (conj xy nxy)) => [ok _]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)