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

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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".
+
+inductive stupidtype: Set \def
+  | Base : stupidtype
+  | Next : stupidtype \to stupidtype
+  | Pair : stupidtype \to stupidtype \to stupidtype.
+  
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "exists" (instance 0) = "Coq's exists".
+alias symbol "or" (instance 0) = "Coq's logical or".
+alias num (instance 0) = "natural number".
+alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
+alias id "refl_equal" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)".
+  
+theorem serious:
+  \forall a:stupidtype.
+    a = Base 
+  \lor 
+    (\exists b:stupidtype.a = Next b) 
+  \lor 
+    (\exists c,d:stupidtype.a = Pair c d).
+intros.
+elim a.
+clear a.left.left.
+  reflexivity.
+clear H.clear a.left.right.
+  exists.exact s.reflexivity.
+clear H.clear H1.clear a.right.
+  exists.exact s.exists.exact s1.reflexivity.  
+qed.
+
+theorem t: 0=0 \to stupidtype.
+ intros; constructor 1.
+qed.
+
+(* In this test "elim 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: let ax \def refl_equal ? 0 in t ax = t ax.
+ elim t; reflexivity.
+qed.
+
+(* This test shows a bug where elim opens a new unus{ed,eful} goal *)
+
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
+
+inductive sum (n:nat) : nat \to nat \to Set \def
+  k: \forall x,y. n = x + y \to sum n x y.
+  
+theorem t': \forall x,y. \forall H: sum x y O.
+          match H with [ (k a b p) \Rightarrow a ] = x.
+ intros.
+ cut (y = y \to O = O \to match H with [ (k a b p) \Rightarrow a] = x).
+ apply Hcut; reflexivity.
+ apply
+  (sum_ind ?
+    (\lambda a,b,K. y=a \to O=b \to
+        match K with [ (k a b p) \Rightarrow a ] = x)
+     ? ? ? H).
+ simplify. intros.
+ generalize in match H1.
+ rewrite < H2; rewrite < H3.intro.
+ rewrite > H4.autobatch library.
+qed.