ocaml 3.09 transition

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

diff --git a/helm/matita/tests/fguidi.ma b/helm/matita/tests/fguidi.ma
index 07e7989ceb38745e55dca3d61b0a9556f0cd180f..567f15c97c88ca976c0ecf8b71b389df700da752 100644 (file)
--- a/helm/matita/tests/fguidi.ma
+++ b/helm/matita/tests/fguidi.ma
@@ -1,4 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/fguidi/".
+include "coq.ma".
 
 alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
@@ -27,7 +42,7 @@ definition pred: nat \to nat \def
       ]. 
 
 theorem eq_gen_S_O: \forall x. (S x = O) \to \forall P:Prop. P.
-intros. apply False_ind. cut (is_S O). auto. elim H. exact I.
+intros. apply False_ind. cut (is_S O). auto paramodulation. elim H. exact I.
 qed.
 
 theorem eq_gen_S_O_cc: (\forall P:Prop. P) \to \forall x. (S x = O).
@@ -35,12 +50,12 @@ intros. auto.
 qed.
 
 theorem eq_gen_S_S: \forall m,n. (S m) = (S n) \to m = n. 
-intros. cut (pred (S m)) = (pred (S n)). 
-assumption. elim H. auto.
+intros. cut ((pred (S m)) = (pred (S n))). 
+assumption. elim H. auto paramodulation.
 qed.
 
 theorem eq_gen_S_S_cc: \forall m,n. m = n \to (S m) = (S n).
-intros. elim H. auto.
+intros. elim H. auto paramodulation.
 qed.
 
 inductive le: nat \to nat \to Prop \def
@@ -48,37 +63,37 @@ inductive le: nat \to nat \to Prop \def
    | le_succ: \forall m, n. (le m n) \to (le (S m) (S n)).
 
 theorem le_refl: \forall x. (le x x).
-intros. elim x. auto. auto.
+intros. elim x. auto paramodulation. auto paramodulation.
 qed.
 
 theorem le_gen_x_O_aux: \forall x, y. (le x y) \to (y =O) \to 
                         (x = O).
-intros 3. elim H. auto. apply eq_gen_S_O. exact n1. auto.
+intros 3. elim H. auto paramodulation. apply eq_gen_S_O. exact n1. auto paramodulation.
 qed.
 
 theorem le_gen_x_O: \forall x. (le x O) \to (x = O).
-intros. apply le_gen_x_O_aux. exact O. auto. auto.
+intros. apply le_gen_x_O_aux. exact O. auto paramodulation. auto paramodulation.
 qed.
 
 theorem le_gen_x_O_cc: \forall x. (x = O) \to (le x O).
-intros. elim H. auto.
+intros. elim H. auto paramodulation.
 qed.
 
 theorem le_gen_S_x_aux: \forall m,x,y. (le y x) \to (y = S m) \to 
                         (\exists n. x = (S n) \land (le m n)).
 intros 4. elim H. 
-apply eq_gen_S_O. exact m. elim H1. auto. 
-cut n = m. elim Hcut. apply ex_intro. exact n1. auto. auto.
+apply eq_gen_S_O. exact m. elim H1. auto paramodulation.
+cut (n = m). elim Hcut. apply ex_intro. exact n1. auto paramodulation. auto. (* paramodulation non trova la prova *)
 qed.
 
 theorem le_gen_S_x: \forall m,x. (le (S m) x) \to 
                     (\exists n. x = (S n) \land (le m n)).
-intros. apply le_gen_S_x_aux. exact (S m). auto. auto.
+intros. apply le_gen_S_x_aux. exact (S m). auto paramodulation. auto paramodulation.
 qed.
 
 theorem le_gen_S_x_cc: \forall m,x. (\exists n. x = (S n) \land (le m n)) \to
                        (le (S m) x).
-intros. elim H. elim H1. cut (S x1) = x. elim Hcut. auto. elim H2. auto.
+intros. elim H. elim H1. cut ((S x1) = x). elim Hcut. auto paramodulation. elim H2. auto paramodulation.
 qed.
 
 theorem le_gen_S_S: \forall m,n. (le (S m) (S n)) \to (le m n).
@@ -88,12 +103,12 @@ lapply eq_gen_S_S to H2 using H4. rewrite > H4. assumption.
 qed.
 
 theorem le_gen_S_S_cc: \forall m,n. (le m n) \to (le (S m) (S n)).
-intros. auto.
+intros. auto paramodulation.
 qed.
 
 (*
 theorem le_trans: \forall x,y. (le x y) \to \forall z. (le y z) \to (le x z).
 intros 1. elim x; clear H. clear x. 
-auto.
+auto paramodulation.
 fwd H1 [H]. decompose H.
 *)