qed.
inductive cmp_cases (n,m:nat) : CProp ≝
- | cmp_lt : n < m → cmp_cases n m
- | cmp_eq : n = m → cmp_cases n m
+ | 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|constructor 2|constructor 3] assumption;
+[constructor 1;apply lt_to_le|constructor 1;rewrite > H|constructor 2]
+try assumption; apply le_n;
qed.