more work on dama

[helm.git] / helm / software / matita / library / nat / compare.ma

diff --git a/helm/software/matita/library/nat/compare.ma b/helm/software/matita/library/nat/compare.ma
index c01f089bd57005e7168515615f0e5414df8fb221..4c44c74e0b61e8e84faea821e7b771b8dab56759 100644 (file)
--- a/helm/software/matita/library/nat/compare.ma
+++ b/helm/software/matita/library/nat/compare.ma
@@ -319,12 +319,12 @@ apply ((H2 H3)).
 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.