proposition: Lemma eqidP m n (I : 'cV[R]_m) (J : 'cV[R]_n) : reflect (I :=: J)%IS (I == J)%IS.
proof: Proof. apply: (iffP andP) => [[sIJ sJI] p K | eqIJ]; last by rewrite !eqIJ. by split; apply/idP/idP; by [move/subid_trans->|move/(subid_trans _)->]. 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