From de21be5819bd35a2cb83b3d33b1c578d970a32c7 Mon Sep 17 00:00:00 2001
From: marangon <??>
Date: Thu, 15 Dec 2005 16:03:01 +0000
Subject: [PATCH] New tactic: inversion.  - only first phase implemented (no
 cleaning)   - code in inversion.ml to be improved/cleaned up

---
 helm/matita/tests/inversion.ma  | 68 ++++++++++++++++++---------------
 helm/matita/tests/inversion2.ma | 44 +++++++++++++++++++++
 2 files changed, 82 insertions(+), 30 deletions(-)
 create mode 100644 helm/matita/tests/inversion2.ma

diff --git a/helm/matita/tests/inversion.ma b/helm/matita/tests/inversion.ma
index f717cd1df..b39d839b0 100644
--- a/helm/matita/tests/inversion.ma
+++ b/helm/matita/tests/inversion.ma
@@ -12,42 +12,50 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/tests/inversion/".
+set "baseuri" "cic:/matita/tests/inversion_sum/".
 include "coq.ma".
 
-inductive nat : Set \def
-   O : nat
- | S : nat \to nat.
- 
-inductive le (n:nat) : nat \to Prop \def
-   leO : le n n
- | leS : \forall m. le n m \to le n (S m).
 
 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 test_inversion: \forall n. le n O \to n=O.
+  
+theorem t: \forall x,y. \forall H: sum x y O.
+          match H with [ (k a b p) \Rightarrow a ] = x.
  intros.
- (* inversion begins *)
- cut (O=O);
- [ 2: reflexivity;
- | generalize in match Hcut.
-   apply (le_ind ? (\lambda x. O=x \to n=x) ? ? ? H);
-   [ intro. rewrite < H1. clear Hcut.
-   | simplify. intros. discriminate H3.
-   ]
-  reflexivity.
- ]
+ inversion H.
+ 
+ (*
+ 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).
+ goal 16.*)
+ simplify. intros.
+ generalize in match H1.
+ rewrite < H2; rewrite < H3.intro.
+ rewrite > H4.auto.
 qed.
 
-(* Piu' semplice e non lascia l'ipotesi inutile Hcut *)
-alias id "refl_equal" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)".
-theorem test_inversion2: \forall n. le n O \to n=O.
- intros.
- (* inversion begins *)
- generalize in match (refl_equal nat O).
- apply (le_ind ? (\lambda x. O=x \to n=x) ? ? ? H);
- [ intro. rewrite < H1.
- | simplify. intros. discriminate H3.
- ]
- reflexivity.
+theorem t1: \forall x,y. sum x y O \to x = y.
+intros.
+
+(*
+cut y=y \to O=O \to x = y.
+apply Hcut.reflexivity. reflexivity.
+apply (sum_ind ? (\lambda a,b,K. y=a \to O=b \to x=a) ? ? ? s).*)
+
+(*apply (sum_ind ? (\lambda a,b,K. y = a \to O = b \to  x = a) ? ? ? s).*)
+inversion s.
+intros.simplify.
+intros.
+rewrite > H. rewrite < H2.  auto.
 qed.
diff --git a/helm/matita/tests/inversion2.ma b/helm/matita/tests/inversion2.ma
new file mode 100644
index 000000000..bb8d18980
--- /dev/null
+++ b/helm/matita/tests/inversion2.ma
@@ -0,0 +1,44 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/inversion/".
+include "coq.ma".
+
+inductive nat : Set \def
+   O : nat
+ | S : nat \to nat.
+
+
+inductive le (n:nat) : nat \to Prop \def
+   leO : le n n
+ | leS : \forall m. le n m \to le n (S m).
+ 
+
+inductive ledx : nat \to nat \to Prop \def
+   ledxO : \forall n. ledx n n
+ | ledxS : \forall m.\forall n. ledx n m \to ledx n (S m).
+
+
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+
+theorem test_inversion: \forall n. le n O \to n=O.
+ intros.
+ inversion H.
+ (* cut n=n \to O=O \to n=O.
+  apply Hcut; reflexivity. *)
+  (* elim H. BUG DI UNSHARING *)
+  (*apply (ledx_ind (\lambda x.\lambda y.  n=x \to O=y \to x=y) ? ? ? ? H).*)
+    simplify. intros. reflexivity.    
+    simplify. intros. discriminate H3.
+qed.
-- 
2.39.2