--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+
+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 id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
+alias id "plus_comm" = "cic:/Coq/Arith/Plus/plus_comm.con".
+
+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.
+