ocaml 3.09 transition

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

diff --git a/helm/matita/tests/rewrite.ma b/helm/matita/tests/rewrite.ma
index e99d75e837ca2140ea67287e4b9203170d267de4..a69e33d77c73915f30470fb3f11537df0695b1fc 100644 (file)
--- a/helm/matita/tests/rewrite.ma
+++ b/helm/matita/tests/rewrite.ma
@@ -1,9 +1,64 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rewrite/".
+include "coq.ma".
+
 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
 alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality". 
+alias symbol "plus" (instance 0) = "Coq's natural plus".
+alias id "plus_n_O" = "cic:/Coq/Init/Peano/plus_n_O.con".
+
 theorem a:
   \forall a,b:nat.
-  a = b \to b + 0 = a.
+  a = b \to b + a + b + a= (\lambda j.((\lambda w.((\lambda x.x + b + w + j) a)) b)) a.
 intros.
-rewrite left H.
\ No newline at end of file
+rewrite < H in \vdash (? ? ? ((\lambda j.((\lambda w.%) ?)) ?)).
+
+rewrite < H in \vdash (? ? % ?).
+
+simplify in \vdash (? ? ? ((\lambda _.((\lambda _.%) ?)) ?)).
+
+rewrite < H in \vdash (? ? ? (% ?)).
+simplify.
+reflexivity.
+qed.
+ 
+theorem t: \forall n. 0=0 \to n = n + 0.
+ intros.
+ apply plus_n_O.
+qed.
+
+(* In this test "rewrite < t" should open a new goal 0=0 and put it in *)
+(* the goallist so that the THEN tactical closes it using reflexivity. *)
+theorem foo: \forall n. n = n + 0.
+ intros.
+ rewrite < t; reflexivity.
+qed.
+
+theorem test_rewrite_in_hyp:
+          \forall n,m. n + 0 = m \to m = n + 0 \to n=m \land m+0=n+0.
+ intros.
+ rewrite < plus_n_O in H.
+ rewrite > plus_n_O in H1.
+ split; [ exact H | exact H1].
+qed.
+
+theorem test_rewrite_in_hyp2:
+          \forall n,m. n + 0 = m \to n + 0 = m \to n=m \land n+0=m.
+ intros.
+ rewrite < plus_n_O in H H1 \vdash (? ? %).
+ split; [ exact H | exact H1].
+qed.