proposition: Lemma csum_of_oddP n m: oddp n -> natp m -> (evenp (n +c m) <-> oddp m).
proof: Proof. move => on mN; split => h; last by apply:csum_of_odd. case: (p_or_not_p (evenp m)) => // h'. by move: (proj2(csum_of_even_odd h' on)); rewrite csumC. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)