intros p q r t H'; elim H'; simpl in |- *; auto with arith.
elim p; simpl in |- *; auto with arith.
intros n H m H0 H1 H2; apply plus_le_compat; auto with arith.
apply le_trans with (m := r + n * r); auto with arith.
Qed.
Hint Resolve lte_comp_mult: arith.

(* Specifications: *)
Theorem le_refl_eq : forall n m : nat, n = m -> n <= m.
intros n m H'; rewrite H'; auto.