proposition: Lemma oprod2_2int a b: natp a -> natp b -> a *o b = a *c b.
proof: Proof. move=> aN bN;move: b bN. have oa:= OS_nat aN. apply: Nat_induction; first by rewrite cprod0r oprod0r. move=> n nN hrec. rewrite (cprod_nS _ nN) (succ_of_nat nN) - (osum2_2int (NS_prod aN nN) aN). by rewrite (oprod2_succ oa (OS_cardinal (CS_nat nN))) hrec. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)