Dummy dependent types are no longer cleaned in inductive type arities.

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

diff --git a/helm/software/matita/library/nat/times.ma b/helm/software/matita/library/nat/times.ma
index 24a2846d7a684eb337f932d502fcc6fb9dab206f..57dc60c6f2a071b5e25400161da998fa88f12763 100644 (file)
--- a/helm/software/matita/library/nat/times.ma
+++ b/helm/software/matita/library/nat/times.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/times".
-
 include "nat/plus.ma".
 
 let rec times n m \def 
@@ -21,7 +19,6 @@ let rec times n m \def
  [ O \Rightarrow O
  | (S p) \Rightarrow m+(times p m) ].
 
-(*CSC: the URI must disappear: there is a bug now *)
 interpretation "natural times" 'times x y = (cic:/matita/nat/times/times.con x y).
 
 theorem times_n_O: \forall n:nat. O = n*O.
@@ -68,6 +65,27 @@ rewrite < plus_n_O.
 reflexivity.
 qed.
 
+alias num (instance 0) = "natural number".
+lemma times_SSO: \forall n.2*(S n) = S(S(2*n)).
+intro.simplify.rewrite < plus_n_Sm.reflexivity.
+qed.
+
+theorem or_eq_eq_S: \forall n.\exists m. 
+n = (S(S O))*m \lor n = S ((S(S O))*m).
+intro.elim n
+  [apply (ex_intro ? ? O).
+   left.reflexivity
+  |elim H.elim H1
+    [apply (ex_intro ? ? a).
+     right.apply eq_f.assumption
+    |apply (ex_intro ? ? (S a)).
+     left.rewrite > H2.
+     apply sym_eq.
+     apply times_SSO
+    ]
+  ]
+qed.
+
 theorem symmetric_times : symmetric nat times. 
 unfold symmetric.
 intros.elim x.