proposition: Lemma order_cp2 x y: worder x -> worder y -> sub x y -> ordinal x <=o ordinal y.
proof: Proof. move => wo1 wo2 xy. have [pa pb]:= (order_cp1 wo1 wo2 xy). suff: x <=O y by move /(order_le_compatible1 wo1 wo2) /ordinal_le_P0. split; fprops; exists (identity (substrate x)), (substrate x); split => //. rewrite -pb; apply: identity_is; fprops. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)