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[helm.git] / helm / matita / tests / simpl.ma

diff --git a/helm/matita/tests/simpl.ma b/helm/matita/tests/simpl.ma
index d77f91fcd0974043b22bb1a55fe3a178f6016d53..2a860e1906078f25b5ae793d107e7fe0370c169b 100644 (file)
--- a/helm/matita/tests/simpl.ma
+++ b/helm/matita/tests/simpl.ma
@@ -1,7 +1,27 @@
-set "baseuri" "cic:/matita/tests/".
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.
@@ -12,3 +32,17 @@ intro. apply H.
 symmetry.
 exact H1.
 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.
+