proposition: Lemma pmc_distrib_left : forall dim m1 m2 (c:vector dim), prod_mat_col _ (sum_matrix _ m1 m2) c ==v sum_vector _ (prod_mat_col dim m1 c) (prod_mat_col _ m2 c).
proof: Proof. apply pmc_distrib_left with (eq:=eq) (plus:=plus) (mult:=mult). apply eq_Equivalence. intros;ring. intros;ring. intros;ring. intros;ring. apply plus_morph. Qed.
imports: Coq(Lia List Setoid Peano_dec Eqdep_dec Ring Zwf Morphisms ZArith) CoLoR(interp)