proposition: Lemma val_submodJ m (W : 'M_(m, \rank U)) x : x \in G -> val_submod (W *m submod_mx Umod x) = val_submod W *m rG x.
proof: Proof. move=> Gx; rewrite 2!(mulmxA W) -val_submodE in_submodK //. by rewrite mxmodule_trans ?val_submodP. 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)