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. fix pcr_distrib_left 1. intros [|dim]. simpl. intros. apply mult_distrib_left. simpl vector. intros [a1 c1] [a2 c2] [a r]. simpl. refine (conj _ (conj _ (conj _ _ ))). apply mult_distrib_left. apply psv_distrib_left. apply psv_distrib_right. apply pcr_distrib_left. Qed.
imports: Coq(Lia List Setoid Peano_dec Eqdep_dec Ring Zwf Morphisms ZArith) CoLoR(interp)