proposition: Lemma ordinal_finite1: finite_set x -> finite_o x.
proof: Proof. move => fsx;split => //. move/(omega_P1 ox)=> infc. move: (sub_finite_set infc fsx) =>/finite_c_P2. by rewrite (card_card CS_omega); case. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)