removed no longer used METAs

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

diff --git a/helm/matita/tests/inversion.ma b/helm/matita/tests/inversion.ma
index f5ad10c7fc727fb33377c9150cad16926030786b..3e49e06685d22818abd961fec9774f7708b4ab79 100644 (file)
--- a/helm/matita/tests/inversion.ma
+++ b/helm/matita/tests/inversion.ma
@@ -1,48 +1,61 @@
-set "baseuri" "cic:/matita/tests/".
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
 
-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).
+set "baseuri" "cic:/matita/tests/inversion_sum/".
+include "legacy/coq.ma".
+
+
+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.
 
-alias symbol "eq" (instance 0) = "leibnitz's equality".
 
-theorem test_inversion: \forall n. le n O \to n=O.
- intros.
- (* inversion begins *)
- cut O=O.
-  (* goal 2: 0 = 0 *)
-  goal 7. reflexivity.
-  (* goal 1 *)
-  generalize Hcut.
-  apply (le_ind ? (\lambda x. O=x \to n=x) ? ? ? H).
-  (* first goal (left open) *)
-  intro. rewrite < H1.
-  clear Hcut.
-  (* second goal (closed) *)
-  goal 14.
-  simplify. intros.
-  discriminate H3.
-  (* inversion ends *)
-  reflexivity.
-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.
+  
+theorem t: \forall x,y. \forall H: sum x y O.
+          match H with [ (k a b p) \Rightarrow a ] = x.
  intros.
- (* inversion begins *)
- generalize (refl_equal nat O).
- apply (le_ind ? (\lambda x. O=x \to n=x) ? ? ? H).
- (* first goal (left open) *)
- intro. rewrite < H1.
- (* second goal (closed) *)
- goal 13.
+ 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.
- discriminate H3.
- (* inversion ends *)
- reflexivity.
+ generalize in match H1.
+ rewrite < H2; rewrite < H3.intro.
+ rewrite > H4.auto.
+qed.
+
+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.