proposition: Lemma NS_prod a b: natp a -> natp b -> natp (a *c b).
proof: Proof. move=> aN bN. move: b bN; apply: Nat_induction; first by rewrite cprod0r; fprops. by move=> n nN mN; rewrite cprod_nS; fprops; apply: NS_sum. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)