proposition: Lemma csum_of_even_odd a b: evenp a -> oddp b -> oddp (a +c b).
proof: Proof. move => [aN ae] /oddp_alt [bN bo]. apply/(oddp_alt); split;first exact:(NS_sum aN bN). by rewrite (crem_sum NS2 card2_nz aN bN) ae bo (csum0l CS1) crem_12. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)