proposition: Lemma UT_nkbin n k: T_nkbin n k.+1 + U_nkbin n.+1 k = T_nkbin n.+1 k.+1.
proof: Proof. rewrite /T_nkbin /U_nkbin !addSn ! addnS doubleS addnCA -addnA addnA -!binS. by congr (_ + _); rewrite addnC - binS. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)