proposition: Lemma quo_mx_coset x : x \in G -> quo_mx krH nHG (coset H x) = rG x.
proof: Proof. move=> Gx; rewrite /quo_mx val_coset ?nHGs //; case: repr_rcosetP => z Hz. by case/rkerP: (subsetP krH z Hz) => Gz rz1; rewrite repr_mxM // rz1 mul1mx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)