proposition: Lemma cprod_inf1 a b: b <=c a -> infinite_c a -> a *c b <=c a.
proof: Proof. move =>leba ia. case: (equal_or_not b \0c) => h. rewrite h cprod0r; apply: (cle_fin_inf finite_0 ia). rewrite (cprod_inf leba ia h); exact (cleR (proj1 ia)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)