proposition: Lemma cnext_pr5P x : cardinalp x -> forall y, (x <c y <-> cnext x <=c y).
proof: Proof. move => cx; split => h. by apply: (proj33 (cnext_pr1 cx)). exact:(clt_leT (cnext_pr2 cx) h). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)