some more work on q

[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 b002d78cccdedd6ad690ffeea67aaa0402c14288..c01f089bd57005e7168515615f0e5414df8fb221 100644 (file)
--- a/helm/software/matita/library/nat/compare.ma
+++ b/helm/software/matita/library/nat/compare.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/compare".
-
 include "datatypes/bool.ma".
 include "datatypes/compare.ma".
 include "nat/orders.ma".
@@ -319,3 +317,14 @@ apply ((H H3)).
 apply ((H1 H3)).
 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_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;
+qed.