From 208a0f7bfa5249f9795e6e225f309cbe715c0fad Mon Sep 17 00:00:00 2001
From: Samuel Mimram <smimram@debian.org>
Date: Tue, 21 Nov 2006 21:38:49 +0000
Subject: Imported Upstream version 8.1~gamma

---
 test-suite/success/unification.v | 65 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 65 insertions(+)
 create mode 100644 test-suite/success/unification.v

(limited to 'test-suite/success/unification.v')

diff --git a/test-suite/success/unification.v b/test-suite/success/unification.v
new file mode 100644
index 00000000..68869621
--- /dev/null
+++ b/test-suite/success/unification.v
@@ -0,0 +1,65 @@
+(* Test patterns unification *)
+
+Lemma l1 : (forall P, (exists x:nat, P x) -> False) 
+         -> forall P, (exists x:nat, P x /\ P x) -> False.
+Proof.
+intros; apply (H _ H0).
+Qed.
+
+Lemma l2 :  forall A:Set, forall Q:A->Set,
+           (forall (P: forall x:A, Q x -> Prop), 
+                   (exists x:A, exists y:Q x, P x y) -> False) 
+         -> forall (P: forall x:A, Q x -> Prop), 
+                   (exists x:A, exists y:Q x, P x y /\ P x y) -> False.
+Proof.
+intros; apply (H _ H0).
+Qed.
+
+
+(* Example submitted for Zenon *)
+
+Axiom zenon_noteq : forall T : Type, forall t : T, ((t <> t) -> False).
+Axiom zenon_notall : forall T : Type, forall P : T -> Prop,
+  (forall z : T, (~(P z) -> False)) -> (~(forall x : T, (P x)) -> False).
+
+  (* Must infer "P := fun x => x=x" in zenon_notall *)
+Check (fun _h1 => (zenon_notall nat _ (fun _T_0 =>
+          (fun _h2 => (zenon_noteq _ _T_0 _h2))) _h1)).
+
+
+(* Core of an example submitted by Ralph Matthes (#849)
+
+   It used to fail because of the K-variable x in the type of "sum_rec ..."
+   which was not in the scope of the evar ?B. Solved by a head
+   beta-reduction of the type "(fun _ : unit + unit => L unit) x" of
+   "sum_rec ...". Shall we used more reduction when solving evars (in
+   real_clean)?? Is there a risk of starting too long reductions?
+
+   Note that the example originally came from a non re-typable
+   pretty-printed term (the checked term is actually re-printed the
+   same form it is checked).  
+*)
+
+Set Implicit Arguments.
+Inductive L (A:Set) : Set := c : A -> L A.
+Parameter f: forall (A:Set)(B:Set), (A->B) -> L A -> L B.
+Parameter t: L (unit + unit).
+
+Check (f (fun x : unit + unit =>
+  sum_rec (fun _ : unit + unit => L unit)
+    (fun y => c y) (fun y => c y) x) t).
+
+
+(* Test patterns unification in apply *)
+
+Require Import Arith.
+Parameter x y : nat.
+Parameter G:x=y->x=y->Prop.
+Parameter K:x<>y->x<>y->Prop.
+Lemma l3 : (forall f:x=y->Prop, forall g:x<>y->Prop,
+            match eq_nat_dec x y with left a => f a | right a => g a end)
+   -> match eq_nat_dec x y with left a => G a a | right a => K a a end.
+Proof.
+intros.
+apply H.
+Qed.
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