proposition: Lemma sub_addidl m n p (I: 'cV[R]_m) (J: 'cV[R]_n) (K: 'cV[R]_p): (J <= K)%IS -> (I +i J <= I +i K)%IS.
proof: Proof. case/subidP => D hD; apply/subidP. exists (block_mx 1%:M 0 0 D). by rewrite hD mul_block_col mul1mx !mul0mx addr0 add0r. 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