added library_auto/ to tests.

[helm.git] / helm / software / matita / library_auto / nat / times.ma

diff --git a/helm/software/matita/library_auto/nat/times.ma b/helm/software/matita/library_auto/nat/times.ma
deleted file mode 100644 (file)
index 60ebc03..0000000
--- a/helm/software/matita/library_auto/nat/times.ma
+++ /dev/null
@@ -1,131 +0,0 @@
-(**************************************************************************)
-(*       __                                                               *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
-(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU Lesser General Public License Version 2.1         *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/library_auto/nat/times".
-
-include "nat/plus.ma".
-
-let rec times n m \def 
- match n with 
- [ O \Rightarrow O
- | (S p) \Rightarrow m+(times p m) ].
-
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "natural times" 'times x y = (cic:/matita/library_auto/nat/times/times.con x y).
-
-theorem times_n_O: \forall n:nat. O = n*O.
-intros.elim n
-[ auto
-  (*simplify.
-  reflexivity.*)
-| simplify.  (* qui auto non funziona: Uncaught exception: Invalid_argument ("List.map2")*)
-  assumption.
-]
-qed.
-
-theorem times_n_Sm : 
-\forall n,m:nat. n+(n*m) = n*(S m).
-intros.elim n
-[ auto.
-  (*simplify.reflexivity.*)
-| simplify.
-  auto
-  (*apply eq_f.
-  rewrite < H.
-  transitivity ((n1+m)+n1*m)
- [ symmetry.                    
-   apply assoc_plus.            
- | transitivity ((m+n1)+n1*m)
-   [ apply eq_f2.
-     apply sym_plus.
-     reflexivity.
-   | apply assoc_plus.
-   ]
- ]*)
-]
-qed.
-
-(* NOTA:
-   se non avessi semplificato con auto tutto il secondo ramo della tattica
-   elim n, avrei comunque potuto risolvere direttamente con auto entrambi
-   i rami generati dalla prima applicazione della tattica transitivity
-   (precisamente transitivity ((n1+m)+n1*m)
- *)
-
-theorem times_n_SO : \forall n:nat. n = n * S O.
-intros.
-rewrite < times_n_Sm.
-auto paramodulation. (*termina la dim anche solo con auto*)
-(*rewrite < times_n_O.
-rewrite < plus_n_O.
-reflexivity.*)
-qed.
-
-theorem times_SSO_n : \forall n:nat. n + n = S (S O) * n.
-intros.
-simplify.
-auto paramodulation. (* termina la dim anche solo con auto*)
-(*rewrite < plus_n_O.
-reflexivity.*)
-qed.
-
-theorem symmetric_times : symmetric nat times. 
-unfold symmetric.
-intros.elim x
-[ auto
-  (*simplify.apply times_n_O.*)
-| simplify.
-  auto
-  (*rewrite > H.apply times_n_Sm.*)
-]
-qed.
-
-variant sym_times : \forall n,m:nat. n*m = m*n \def
-symmetric_times.
-
-theorem distributive_times_plus : distributive nat times plus.
-unfold distributive.
-intros.elim x;simplify
-[ reflexivity.
-| auto
-  (*rewrite > H.
-  rewrite > assoc_plus.
-  rewrite > assoc_plus.
-  apply eq_f.
-  rewrite < assoc_plus. 
-  rewrite < (sym_plus ? z).
-  rewrite > assoc_plus.
-  reflexivity.*)
-]
-qed.
-
-variant distr_times_plus: \forall n,m,p:nat. n*(m+p) = n*m + n*p
-\def distributive_times_plus.
-
-theorem associative_times: associative nat times.
-unfold associative.intros.
-elim x;simplify
-[ apply refl_eq
-| auto
-  (*rewrite < sym_times.
-  rewrite > distr_times_plus.
-  rewrite < sym_times.
-  rewrite < (sym_times (times n y) z).
-  rewrite < H.
-  apply refl_eq.*)
-]
-qed.
-
-variant assoc_times: \forall n,m,p:nat. (n*m)*p = n*(m*p) \def
-associative_times.