proposition: Lemma pcr_distrib_left : forall dim c1 c2 (r:vector dim), prod_col_row _ (sum_vector _ c1 c2) r ==m sum_matrix _ (prod_col_row dim c1 r) (prod_col_row _ c2 r).
proof: Proof. apply pcr_distrib_left with (eq:=eq) (plus:=plus) (mult:=mult). intros;ring. intros;ring. Qed.
imports: Coq(Lia List Setoid Peano_dec Eqdep_dec Ring Zwf Morphisms ZArith) CoLoR(interp)