proposition: Lemma rker_factmod : rker rG \subset rker rU'.
proof: Proof. apply/subsetP=> x /rkerP[Gx cVx]. by rewrite inE Gx /= /factmod_mx cVx mul1mx mulmx1 val_factmodK. 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)