X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fmatita%2Ftests%2Fsimpl.ma;h=2a860e1906078f25b5ae793d107e7fe0370c169b;hb=28ac70d3f475442cda4ef30e0e9c0e6d012b2527;hp=8b0f1a6a0196ab225cf00b546f12e52d019aaff7;hpb=7fb4b063ed9488bbffa34d1cd193fca6c288a425;p=helm.git

diff --git a/helm/matita/tests/simpl.ma b/helm/matita/tests/simpl.ma
index 8b0f1a6a0..2a860e190 100644
--- a/helm/matita/tests/simpl.ma
+++ b/helm/matita/tests/simpl.ma
@@ -1,5 +1,27 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/tests/simpl/".
+include "coq.ma".
+
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias id "plus" = "cic:/Coq/Init/Peano/plus.con".
+alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
+alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
 alias id "not" = "cic:/Coq/Init/Logic/not.con".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+
+
 theorem a : 
  \forall A:Set.
  \forall x,y : A.
@@ -9,4 +31,18 @@ simplify.
 intro. apply H.
 symmetry.
 exact H1.
-qed.
\ No newline at end of file
+qed.
+
+theorem t: let f \def \lambda x,y. x y in f (\lambda x.S x) O = S O.
+ intros. simplify. change in \vdash (? ? (? %) ?) with O. 
+ reflexivity. qed.
+ 
+theorem X: \forall x:nat. let myplus \def plus x in myplus (S O) = S x.
+ intros. simplify. change in \vdash (? ? (% ?) ?) with plus x.
+ rewrite > plus_comm. reflexivity. qed.
+ 
+theorem R: \forall x:nat. let uno \def x + O in S O + uno = 1 + x.
+ intros. simplify.
+  change in \vdash (? ? (? %) ?) with x + O.
+  rewrite > plus_comm. reflexivity. qed.
+