proposition: Lemma commMgJ x y z : [~ x * y, z] = [~ x, z] ^ y * [~ y, z].
proof: Proof. by rewrite !commgEr conjgM mulgA -conjMg mulgK. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat fintype) mathcomp(bigop finset binomial fingroup morphism) mathcomp(automorphism quotient gfunctor)