From cee763a744e6f75bb5c174f809a4fe25f9071a0c Mon Sep 17 00:00:00 2001
From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Thu, 20 Jul 2006 11:22:15 +0000
Subject: [PATCH] reorganization

---
 .../matita/library/nat/div_and_mod.ma         | 14 +++++++
 helm/software/matita/library/nat/primes1.ma   | 38 -------------------
 .../matita/library/nat/sigma_and_pi.ma        |  1 -
 3 files changed, 14 insertions(+), 39 deletions(-)
 delete mode 100644 helm/software/matita/library/nat/primes1.ma

diff --git a/helm/software/matita/library/nat/div_and_mod.ma b/helm/software/matita/library/nat/div_and_mod.ma
index 2f186dd31..a9f40cc89 100644
--- a/helm/software/matita/library/nat/div_and_mod.ma
+++ b/helm/software/matita/library/nat/div_and_mod.ma
@@ -296,3 +296,17 @@ qed.
 
 variant inj_times_l1:\forall n. O < n \to \forall p,q:nat.p*n = q*n \to p=q
 \def lt_O_to_injective_times_l.
+
+(* n_divides computes the pair (div,mod) *)
+
+(* p is just an upper bound, acc is an accumulator *)
+let rec n_divides_aux p n m acc \def
+  match n \mod m with
+  [ O \Rightarrow 
+    match p with
+      [ O \Rightarrow pair nat nat acc n
+      | (S p) \Rightarrow n_divides_aux p (n / m) m (S acc)]
+  | (S a) \Rightarrow pair nat nat acc n].
+
+(* n_divides n m = <q,r> if m divides n q times, with remainder r *)
+definition n_divides \def \lambda n,m:nat.n_divides_aux n n m O.
diff --git a/helm/software/matita/library/nat/primes1.ma b/helm/software/matita/library/nat/primes1.ma
deleted file mode 100644
index 3ec61ee4a..000000000
--- a/helm/software/matita/library/nat/primes1.ma
+++ /dev/null
@@ -1,38 +0,0 @@
-(**************************************************************************)
-(*       ___	                                                            *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
-(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
-(*      \   /                                                             *)
-(*       \ /        Matita is distributed under the terms of the          *)
-(*        v         GNU Lesser General Public License Version 2.1         *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/nat/primes1".
-
-include "datatypes/constructors.ma".
-include "nat/primes.ma".
-
-(* p is just an upper bound, acc is an accumulator *)
-let rec n_divides_aux p n m acc \def
-  match n \mod m with
-  [ O \Rightarrow 
-    match p with
-      [ O \Rightarrow pair nat nat acc n
-      | (S p) \Rightarrow n_divides_aux p (n / m) m (S acc)]
-  | (S a) \Rightarrow pair nat nat acc n].
-
-(* n_divides n m = <q,r> if m divides n q times, with remainder r *)
-definition n_divides \def \lambda n,m:nat.n_divides_aux n n m O.
-
-(*
-theorem n_divides_to_Prop: \forall n,m,p,a. 
-  match n_divides_aux p n m a with
-  [ (pair q r) \Rightarrow n = m \sup a *r].
-intros.
-apply nat_case (n \mod m). *)
-
diff --git a/helm/software/matita/library/nat/sigma_and_pi.ma b/helm/software/matita/library/nat/sigma_and_pi.ma
index 4f5f6cba0..fe3a2d8b5 100644
--- a/helm/software/matita/library/nat/sigma_and_pi.ma
+++ b/helm/software/matita/library/nat/sigma_and_pi.ma
@@ -15,7 +15,6 @@
 set "baseuri" "cic:/matita/nat/sigma_and_pi".
 
 include "nat/factorial.ma".
-include "nat/lt_arith.ma".
 include "nat/exp.ma".
 
 let rec sigma n f m \def
-- 
2.39.2