proposition: Lemma bigcprodW I (r : seq I) P F G : \big[cprod/1]_(i <- r | P i) F i = G -> \prod_(i <- r | P i) F i = G.
proof: Proof. elim/big_rec2: _ G => // i A B _ IH G /cprodP[[_ H _ defB] <- _]. by rewrite (IH H) defB. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)