Many files added. Symbolic links missing. examples and contrib missing due

[helm.git] / helm / EXPORT / exportprove / prove / provaIota.v

diff --git a/helm/EXPORT/exportprove/prove/provaIota.v b/helm/EXPORT/exportprove/prove/provaIota.v
new file mode 100644 (file)
index 0000000..74a510b
--- /dev/null
+++ b/helm/EXPORT/exportprove/prove/provaIota.v
@@ -0,0 +1,53 @@
+Inductive bool : Set := true : bool | false : bool.
+Inductive nat  : Set := O : nat | S : nat -> nat.
+
+Fixpoint plus [n:nat] : nat -> nat :=
+  [m:nat]
+  Cases n of
+     O     => m
+   | (S n) => (S (plus n m))
+  end.
+
+Fixpoint mult [n:nat] : nat -> nat :=
+  [m:nat]
+  Cases n of
+     O     => O
+   | (S n) => (plus m (mult n m))
+  end.
+
+Fixpoint fact [n:nat] : nat  :=
+  Cases n of
+     O     => (S O)
+   | (S n) => (mult (S n) (fact n))
+  end.
+
+Definition bnot :=
+ [b:bool]
+ Cases b of
+    true  => false
+  | false => true
+ end.
+
+Fixpoint is_even [n:nat] : bool :=
+  Cases n of
+     O     => true
+   | (S n) => (bnot (bnot (is_odd n)))
+  end
+with is_odd [n:nat] : bool :=
+  Cases n of
+     O     => false
+   | (S n) => (bnot (bnot (is_even n)))
+  end
+.
+
+Fixpoint idn [n:nat] : nat :=
+  Cases n of
+     O     => O
+   | (S n) => (S (idn n))
+  end.
+
+Definition test1 := (is_even (S (S O))).
+Definition test2 := (is_even (S (S (S O)))).
+Definition test3 := (idn (idn (S O))).
+Definition test4 := (is_odd (fact (S (S (O))))).
+Definition test5 := (is_odd (fact (S (S (S (S (S (S O)))))))).