proposition: Lemma pmc_comm_sv_left : forall dim (m:matrix dim) (c : vector dim) (a:A), prod_mat_col _ (prod_scal_mat _ a m) c ==v prod_scal_vec _ a (prod_mat_col _ m c).
proof: Proof. apply pmc_comm_sv_left with (eq:=eq) (plus:=plus) (mult:=mult). apply eq_Equivalence. 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)