proposition: Lemma psm_assoc : forall dim c1 c2 (r:matrix dim), prod_scal_mat _ c1 (prod_scal_mat _ c2 r) ==m prod_scal_mat _ (mult c1 c2) r .
proof: Proof. fix psm_assoc 1. intros [|dim]. simpl. intros. symmetry; apply mult_assoc. simpl matrix. intros c1 c2 [a [r [c m]]]. simpl. refine (conj _ (conj _ (conj _ _ ))). symmetry; apply mult_assoc. apply psv_assoc. apply psv_assoc. apply psm_assoc. Qed.
imports: Coq(Lia List Setoid Peano_dec Eqdep_dec Ring Zwf Morphisms ZArith) CoLoR(interp)