- renamed ocaml/ to components/

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

diff --git a/helm/matita/tests/fguidi.ma b/helm/matita/tests/fguidi.ma
deleted file mode 100644 (file)
index c6eb2a9..0000000
--- a/helm/matita/tests/fguidi.ma
+++ /dev/null
@@ -1,114 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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 "legacy/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)".
-alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
-alias id "le" = "cic:/matita/fguidi/le.ind#xpointer(1/1)".
-alias id "False_ind" = "cic:/Coq/Init/Logic/False_ind.con".
-alias id "I" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1/1)". 
-alias id "ex_intro" = "cic:/Coq/Init/Logic/ex.ind#xpointer(1/1/1)".
-alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
-alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
-
-alias symbol "and" (instance 0) = "Coq's logical and".
-alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
-alias symbol "exists" (instance 0) = "Coq's exists".
-
-definition is_S: nat \to Prop \def
-   \lambda n. match n with 
-      [ O     \Rightarrow False
-      | (S n) \Rightarrow True
-      ].
-
-definition pred: nat \to nat \def
-   \lambda n. match n with
-      [ O     \Rightarrow O
-      | (S n) \Rightarrow n
-      ]. 
-
-theorem eq_gen_S_O: \forall x. (S x = O) \to \forall P:Prop. P.
-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).
-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 paramodulation.
-qed.
-
-theorem eq_gen_S_S_cc: \forall m,n. m = n \to (S m) = (S n).
-intros. elim H. auto paramodulation.
-qed.
-
-inductive le: nat \to nat \to Prop \def
-     le_zero: \forall n. (le O n)
-   | 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 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 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 paramodulation. auto paramodulation.
-qed.
-
-theorem le_gen_x_O_cc: \forall x. (x = O) \to (le x O).
-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 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 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 paramodulation. elim H2. auto paramodulation.
-qed.
-
-theorem le_gen_S_S: \forall m,n. (le (S m) (S n)) \to (le m n).
-intros.
-lapply le_gen_S_x to H using H0. elim H0. elim H1. 
-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 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 paramodulation.
-fwd H1 [H]. decompose H.
-*)