From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Thu, 28 Jul 2005 10:21:46 +0000 (+0000)
Subject: removed orders_op from library (now in le_arith and lt_arith).
X-Git-Tag: V_0_7_2~24
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=d82900f9e0850c9015ca7f5d226831c85fe073a8;p=helm.git

removed orders_op from library (now in le_arith and lt_arith).
---

diff --git a/helm/matita/library/nat/orders_op.ma b/helm/matita/library/nat/orders_op.ma
deleted file mode 100644
index bfb3668c7..000000000
--- a/helm/matita/library/nat/orders_op.ma
+++ /dev/null
@@ -1,98 +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/nat/orders_op".
-
-include "higher_order_defs/functions.ma".
-include "nat/times.ma".
-include "nat/orders.ma".
-
-(* plus *)
-theorem monotonic_le_plus_r: 
-\forall n:nat.monotonic nat le (\lambda m.n+m).
-simplify.intros.elim n.
-simplify.assumption.
-simplify.apply le_S_S.assumption.
-qed.
-
-theorem le_plus_r: \forall p,n,m:nat. n \leq m \to p+n \leq p+m
-\def monotonic_le_plus_r.
-
-theorem monotonic_le_plus_l: 
-\forall m:nat.monotonic nat le (\lambda n.n+m).
-simplify.intros.
-rewrite < sym_plus.rewrite < sym_plus m.
-apply le_plus_r.assumption.
-qed.
-
-theorem le_plus_l: \forall p,n,m:nat. n \leq m \to n+p \leq m+p
-\def monotonic_le_plus_l.
-
-theorem le_plus: \forall n1,n2,m1,m2:nat. n1 \leq n2  \to m1 \leq m2 
-\to n1+m1 \leq n2+m2.
-intros.
-apply trans_le ? (n2+m1).
-apply le_plus_l.assumption.
-apply le_plus_r.assumption.
-qed.
-
-theorem le_plus_n :\forall n,m:nat. m \leq n+m.
-intros.change with O+m \leq n+m.
-apply le_plus_l.apply le_O_n.
-qed.
-
-theorem eq_plus_to_le: \forall n,m,p:nat.n=m+p \to m \leq n.
-intros.rewrite > H.
-rewrite < sym_plus.
-apply le_plus_n.
-qed.
-
-(* times *)
-theorem monotonic_le_times_r: 
-\forall n:nat.monotonic nat le (\lambda m.n*m).
-simplify.intros.elim n.
-simplify.apply le_O_n.
-simplify.apply le_plus.
-assumption.
-assumption.
-qed.
-
-theorem le_times_r: \forall p,n,m:nat. n \leq m \to p*n \leq p*m
-\def monotonic_le_times_r.
-
-theorem monotonic_le_times_l: 
-\forall m:nat.monotonic nat le (\lambda n.n*m).
-simplify.intros.
-rewrite < sym_times.rewrite < sym_times m.
-apply le_times_r.assumption.
-qed.
-
-theorem le_times_l: \forall p,n,m:nat. n \leq m \to n*p \leq m*p
-\def monotonic_le_times_l.
-
-theorem le_times: \forall n1,n2,m1,m2:nat. n1 \leq n2  \to m1 \leq m2 
-\to n1*m1 \leq n2*m2.
-intros.
-apply trans_le ? (n2*m1).
-apply le_times_l.assumption.
-apply le_times_r.assumption.
-qed.
-
-theorem le_times_n: \forall n,m:nat.S O \leq n \to m \leq n*m.
-intros.elim H.simplify.
-elim (plus_n_O ?).apply le_n.
-simplify.rewrite < sym_plus.apply le_plus_n.
-qed.
-
-