proposition: Lemma mulid_congr m n p q (I: 'cV[R]_m) (J: 'cV[R]_n) (K: 'cV[R]_p) (L: 'cV[R]_q) : (I :=: K)%IS -> (J :=: L)%IS -> (I *i J :=: K *i L)%IS.
proof: Proof. case/eqidP/andP=> h1 h2 /eqidP /andP [h3 h4]; apply/eqidP/andP; split. by apply/(subid_trans (sub_mulidl _ h3))/(sub_mulidr _ h1). by apply/(subid_trans (sub_mulidl _ h4))/(sub_mulidr _ h2). 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