proposition: Lemma bigcprodWY I (r : seq I) P F G : \big[cprod/1]_(i <- r | P i) F i = G -> << \bigcup_(i <- r | P i) F i >> = G.
proof: Proof. elim/big_rec2: _ G => [|i A B _ IH G]; first by rewrite gen0. case/cprodP => [[K H -> defB] <- cKH]. by rewrite -[<<_>>]joing_idr (IH H) ?cent_joinEr -?defB. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)