proposition: Lemma mprodXE {I} (F : I -> 'X_{1..n}) P (r : seq _) : \prod_(i <- r | P i) 'X_[R, F i] = 'X_[\sum_(i <- r | P i) F i].
proof: Proof. rewrite (eq_bigr (fun i => 'X_[R, F i] ^+ 1)) => [|i _]. by rewrite mprodXnE. by rewrite expr1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finfun bigop finset binomial) mathcomp(order fingroup perm ssralg zmodp poly ssrint) mathcomp(matrix vector) mathcomp(bigenough) ssrcomplements freeg