proposition: Lemma subid_mulid_congr m n p o (I : 'cV[R]_m) (J : 'cV[R]_n) (K : 'cV[R]_p) (L : 'cV_o) : (I <= K)%IS -> (J <= L)%IS -> (I *i J <= K *i L)%IS.
proof: Proof. move => h1 h2. by apply/(subid_trans (sub_mulidl _ h2))/(sub_mulidr _ h1). 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