apply ((H1 H3)).
apply ((H2 H3)).
qed.
+
+inductive cmp_cases (n,m:nat) : CProp ≝
+ | cmp_le : n ≤ m → cmp_cases n m
+ | cmp_gt : m < n → cmp_cases n m.
+
+lemma cmp_nat: ∀n,m.cmp_cases n m.
+intros; generalize in match (nat_compare_to_Prop n m);
+cases (nat_compare n m); intros;
+[constructor 1;apply lt_to_le|constructor 1;rewrite > H|constructor 2]
+try assumption; apply le_n;
+qed.