From 5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 Mon Sep 17 00:00:00 2001
From: Stephane Glondu <steph@glondu.net>
Date: Wed, 21 Jul 2010 09:46:51 +0200
Subject: Imported Upstream snapshot 8.3~beta0+13298

---
 plugins/dp/test2.v | 80 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 plugins/dp/test2.v

(limited to 'plugins/dp/test2.v')

diff --git a/plugins/dp/test2.v b/plugins/dp/test2.v
new file mode 100644
index 00000000..0940b135
--- /dev/null
+++ b/plugins/dp/test2.v
@@ -0,0 +1,80 @@
+Require Import ZArith.
+Require Import Classical.
+Require Import List.
+
+Open Scope list_scope.
+Open Scope Z_scope.
+
+Dp_debug.
+Dp_timeout 3.
+Require Export zenon.
+
+Definition neg (z:Z) : Z := match z with
+  | Z0 => Z0
+  | Zpos p => Zneg p
+  | Zneg p => Zpos p
+  end.
+
+Goal forall z, neg (neg z) = z.
+  Admitted.
+
+Open Scope nat_scope.
+Print plus.
+
+Goal forall x, x+0=x.
+  induction x; ergo.
+  (* simplify resoud le premier, pas le second *)
+  Admitted.
+
+Goal 1::2::3::nil = 1::2::(1+2)::nil.
+  zenon.
+  Admitted.
+
+Definition T := nat.
+Parameter fct : T -> nat.
+Goal fct O = O.
+ Admitted.
+
+Fixpoint even (n:nat) : Prop :=
+  match n with
+  O => True
+  | S O => False
+  | S (S p) => even p
+  end.
+
+Goal even 4%nat.
+  try zenon.
+  Admitted.
+
+Definition p (A B:Set) (a:A) (b:B) : list (A*B) := cons (a,b) nil.
+
+Definition head :=
+fun (A : Set) (l : list A) =>
+match l with
+| nil => None (A:=A)
+| x :: _ => Some x
+end.
+
+Goal forall x, head _ (p _ _ 1 2) = Some x -> fst x = 1.
+
+Admitted.
+
+(*
+BUG avec head prédéfini : manque eta-expansion sur A:Set
+
+Goal forall x, head _ (p _ _ 1 2) = Some x -> fst x = 1.
+
+Print value.
+Print Some.
+
+zenon.
+*)
+
+Inductive IN (A:Set) : A -> list A -> Prop :=
+  | IN1 : forall x l, IN A x (x::l)
+  | IN2: forall x l, IN A x l -> forall y, IN A x (y::l).
+Implicit Arguments IN [A].
+
+Goal forall x, forall (l:list nat), IN x l -> IN x (1%nat::l).
+  zenon.
+Print In.
-- 
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