proposition: Lemma sub_mulidl m n p (I: 'cV[R]_m) (J: 'cV[R]_n) (K: 'cV[R]_p): (J <= K -> I *i J <= I *i K)%IS.
proof: Proof. case/subidP => D hD; apply/subidP; exists (lin_mulmxr D^T)^T. rewrite -trmx_mul; apply: (canLR (@trmxK _ _ _)); apply: (canLR vec_mxK). by rewrite trmxK mx_vec_lin /= hD trmx_mul mulmxA. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq path) mathcomp(ssralg fintype perm choice fingroup) mathcomp(matrix bigop zmodp mxalgebra poly) ssrcomplements