1 files changed, 78 insertions, 0 deletions
diff --git a/contrib/dp/test2.v b/contrib/dp/test2.v
new file mode 100644
index 00000000..4e933a3c
--- /dev/null
+++ b/contrib/dp/test2.v
@@ -0,0 +1,78 @@
+Require Import ZArith.
+Require Import Classical.
+Require Import List.
+
+Open Scope list_scope.
+Open Scope Z_scope.
+
+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.
+  zenon.
+  zenon.
+  (* 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.