+(**************************************************************************)
+(* ___ *)
+(* ||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 + a = a + a.
+ a = b \to b + a + b + a= (\lambda j.((\lambda w.((\lambda x.x + b + w + j) a)) b)) a.
intros.
-rewrite right H in (? ? % ?).
+rewrite < H in \vdash (? ? ? ((\lambda j.((\lambda w.%) ?)) ?)).
+
+rewrite < H in \vdash (? ? % ?).
+
+simplify in \vdash (? ? ? ((\lambda _.((\lambda _.%) ?)) ?)).
+
+rewrite < H in \vdash (? ? ? (% ?)).
+simplify.
reflexivity.
-qed.
\ No newline at end of file
+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.