proposition: Lemma in_factmodK m (W : 'M_(m, n)) : (W <= U^C)%MS -> val_factmod (in_factmod W) = W.
proof: Proof. case/submxP=> w ->{W}; rewrite /val_factmod /= -2!mulmxA. congr (_ *m _); rewrite (mulmxA (col_base _)) mulmx_base -2!mulmxA. by rewrite mulKVmx ?row_ebase_unit // mulmxA copid_mx_id ?rank_leq_row. 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)