proposition: Lemma mxcol_sum (I : finType) m (C_ : forall j i, 'M[V]_(p_ i, m)) (P : {pred I}): \mxcol_i (\sum_(j | P j) C_ j i) = \sum_(j | P j) \mxcol_i (C_ j i).
proof: Proof. apply/matrixP => i 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)