simplify and let-in

diff --git a/helm/matita/tests/simpl.ma b/helm/matita/tests/simpl.ma
index dbc4e9c06e54cfbf1c50d7d2345f2d31dd0c236c..2a860e1906078f25b5ae793d107e7fe0370c169b 100644 (file)
--- a/helm/matita/tests/simpl.ma
+++ b/helm/matita/tests/simpl.ma
@@ -15,8 +15,13 @@
 set "baseuri" "cic:/matita/tests/simpl/".
 include "coq.ma".
 
-alias id "not" = "cic:/Coq/Init/Logic/not.con".
 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".
+
+
 theorem a : 
  \forall A:Set.
  \forall x,y : A.
@@ -27,3 +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.
+