proposition: Lemma prm_comm_sv_right : forall dim (r : vector dim) (m:matrix dim) (a:A), prod_row_mat _ r (prod_scal_mat _ a m) ==v prod_scal_vec _ a (prod_row_mat _ r m).
proof: Proof. fix prm_comm_sv_right 1. intros [|dim]. simpl. intros;rewrite <- mult_assoc. rewrite (mult_comm r a). apply mult_assoc. simpl vector;simpl matrix. intros [a1 r1] [a2 [r2 [c2 m2]]] a. simpl. f_equal. rewrite prc_comm_sv_right. repeat rewrite mult_distrib_right. refine (conj _ _). rewrite <- mult_assoc. rewrite (mult_comm a1 a). rewrite mult_assoc. reflexivity. rewrite psv_distrib_right. rewrite psv_comm. rewrite prm_comm_sv_right. reflexivity. Qed.
imports: Coq(Lia List Setoid Peano_dec Eqdep_dec Ring Zwf Morphisms ZArith) CoLoR(interp)