proposition: Lemma submxcol_sum (I : finType) m (C_ : forall j, 'M[V]_(sp, m)) (P : {pred I}) i : submxcol (\sum_(j | P j) C_ j) i = \sum_(j | P j) submxcol (C_ j) i.
proof: Proof. apply/matrixP => j j'; rewrite !(mxE, summxE). by apply: eq_bigr => l; rewrite !mxE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg countalg finalg zmodp)