X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Ftests%2Fapply.ma;h=21c0faa419100b2958493aaee9f697b714c22a9d;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=0fcf73cf32fc81cbf60dc44c4549116e69df5ec9;hpb=9f7cb5462119ce44becf0bc9848d61690a048ac7;p=helm.git

diff --git a/helm/matita/tests/apply.ma b/helm/matita/tests/apply.ma
index 0fcf73cf3..21c0faa41 100644
--- a/helm/matita/tests/apply.ma
+++ b/helm/matita/tests/apply.ma
@@ -1,5 +1,20 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
 (* test _with_ the WHD on the apply argument *)
 set "baseuri" "cic:/matita/tests/apply/".
+include "coq.ma".
 
 alias id "not" = "cic:/Coq/Init/Logic/not.con".
 alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
@@ -14,7 +29,7 @@ qed.
 
 (* test _without_ the WHD on the apply argument *)
 
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
 
 theorem a:
   \forall A:Set.
@@ -23,3 +38,20 @@ theorem a:
 intros.
 apply H.
 qed.
+
+
+(* this test shows what happens when a term of type A -> ? is applied to
+   a goal of type A' -> B: if A unifies with A' the unifier becomes ? := B
+   and no goal is opened; otherwise the unifier becomes ? := A' -> B and a
+   new goal of type A is created. *)
+theorem c:
+ \forall A,B:Prop.
+   A \to (\forall P: Prop. A \to P) \to (A \to B) \land (B \to B).
+ intros 4; split; [ apply H1 | apply H1; exact H ].
+qed.
+
+(* this test requires the delta-expansion of not in the type of the applied
+   term (to reveal a product) *)
+theorem d: \forall A: Prop. \lnot A \to A \to False.
+ intros. apply H. assumption.
+qed.
\ No newline at end of file