proposition: Lemma pm_distrib_left : forall dim m1 m2 (m3:matrix dim), prod_matrix _ (sum_matrix _ m1 m2) m3 ==m sum_matrix _ (prod_matrix dim m1 m3) (prod_matrix _ m2 m3).
proof: Proof. apply pm_distrib_left with (eq:=eq) (plus:=plus) (mult:=mult). apply eq_Equivalence. intros;ring. intros;ring. intros;ring. intros;ring. apply plus_morph. apply mult_morph. Qed.
imports: Coq(Lia List Setoid Peano_dec Eqdep_dec Ring Zwf Morphisms ZArith) CoLoR(interp)