proposition: Theorem Zle_Zmult_comp_l : forall x y z : Z, (0 <= z)%Z -> (x <= y)%Z -> (z * x <= z * y)%Z.
proof: Proof. intros x y z H' H'0; repeat rewrite (Zmult_comm z); apply Zle_Zmult_comp_r; auto. Qed.
imports: Reals ZArith List PeanoNat Psatz