proposition: Lemma bin_mod2_rec1 n k : 'C(n.+2, k.+2) = 'C(n, k.+2) + 'C(n, k) %[mod 2].
proof: Proof. rewrite !binS addnA -(addnA 'C(n, k.+2)) (addnC 'C(n, k.+2)) addnn -muln2. by rewrite - addnA modnMDl. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq choice fintype order bigop ssralg) mathcomp(div ssrnum ssrint rat prime path binomial) mathcomp(tuple finset) gaia(fibm)