proposition: Lemma subid_addid_congr m n p (I : 'cV[R]_n) (J : 'cV[R]_m) (K : 'cV[R]_p) : (I <= K)%IS -> (J <= K)%IS -> (I +i J <= K)%IS.
proof: Proof. case/subidP => C hC /subidP [D hD]; apply/subidP. by exists (col_mx C D); rewrite mul_col_mx -hC -hD. 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