New tactic: inversion.

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

diff --git a/helm/matita/tests/inversion.ma b/helm/matita/tests/inversion.ma
index f717cd1df7f17969a0ca6169cc21833e711f4754..b39d839b00cfe80a56bcd08bee4593cc846d73fc 100644 (file)
--- 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.