Integration of theories/Ints/Z/* in ZArith and large cleanup and extension of Zdiv

Some details: 

 - ZAux.v is the only file left in Ints/Z. The few elements that remain in it
   are rather specific or compatibility oriented. Others parts and files have 
   been either deleted when unused or pushed into some place of ZArith. 
 - Ints/List/ is removed since it was not needed anymore
 - Ints/Tactic.v disappear: some of its tactic were unused, some already in 
   Tactics.v (case_eq, f_equal instead of eq_tac), and the nice contradict 
   has been added to Tactics.v
 - Znumtheory inherits lots of results about Zdivide, rel_prime, prime, Zgcd, ...
 - A new file Zpow_facts inherits lots of results about Zpower. Placing them 
   into Zpower would have been difficult with respect to compatibility 
   (import of ring)
 - A few things added to Zmax, Zabs, Znat, Zsqrt, Zeven, Zorder
 - Adequate adaptations to Ints/num/* (mainly renaming of lemmas) 
 
Now, concerning Zdiv, the behavior when dividing by a negative number is now 
fully proved. When this was possible, existing lemmas has been extended, 
either from strictly positive to non-zero divisor, or even to arbitrary 
divisor (especially when playing with Zmod). These extended lemmas are named
with the suffix _full, whereas the original restrictive lemmas are retained 
for compatibility. Several lemmas now have shorter proofs (based on unicity 
lemmas). Lemmas are now more or less organized by themes (division and order, 
division and usual operations, etc). Three possible choices of spec for 
divisions on negative numbers are presented: this Zdiv, the ocaml approach
and the remainder-always-positive approach. The ugly behavior of Zopp 
with the current choice of Zdiv/Zmod is now fully covered. A embryo of 
division "a la Ocaml" is given: Odiv and Omod. 




git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10291 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 0 insertions, 76 deletions

diff --git a/theories/Ints/Tactic.v b/theories/Ints/Tactic.v
deleted file mode 100644
index 6837f5922..000000000
--- a/theories/Ints/Tactic.v
+++ /dev/null
@@ -1,76 +0,0 @@
-
-(*************************************************************)
-(*      This file is distributed under the terms of the      *)
-(*      GNU Lesser General Public License Version 2.1        *)
-(*************************************************************)
-(*    Benjamin.Gregoire@inria.fr Laurent.Thery@inria.fr      *)
-(*************************************************************)
-
-
-(**********************************************************************
-       Tactic.v                                                                                    
-          Useful tactics                                                                       
- **********************************************************************)
-
-(**************************************
-  A simple tactic to end a proof 
-**************************************)
-Ltac  finish := intros; auto; trivial; discriminate.
-
-
-(**************************************
- A tactic for proof by contradiction
-     with contradict H 
-         H: ~A |-   B      gives           |-   A
-         H: ~A |- ~ B     gives  H: B |-   A
-         H:   A |-   B      gives           |- ~ A
-         H:   A |-   B      gives           |- ~ A
-         H:   A |- ~ B     gives  H: A |- ~ A
-**************************************)
-
-Ltac  contradict name := 
-     let term := type of name in (
-     match term with 
-       (~_) => 
-          match goal with 
-            |- ~ _  => let x := fresh in
-                     (intros x; case name; 
-                      generalize x; clear x name;
-                      intro name)
-          | |- _    => case name; clear name
-          end
-     | _ => 
-          match goal with 
-            |- ~ _  => let x := fresh in
-                    (intros x;  absurd term;
-                       [idtac | exact name]; generalize x; clear x name;
-                       intros name)
-          | |- _    => generalize name; absurd term;
-                       [idtac | exact name]; clear name
-          end
-     end).
-
-
-(**************************************
- A tactic to use f_equal? theorems 
-**************************************)
-
-Ltac eq_tac := 
- match goal with
-       |-  (?g _ = ?g _) => apply f_equal with (f := g)
- |     |-  (?g ?X _ = ?g  ?X _) => apply f_equal with (f := g  X)
- |     |-  (?g _ _ = ?g  _ _) => apply f_equal2 with (f := g)
- |     |-  (?g ?X ?Y _ = ?g ?X ?Y _) => apply f_equal with (f := g X Y)
- |     |-  (?g ?X _ _ = ?g ?X _ _) => apply f_equal2 with (f := g X)
- |     |-  (?g _ _ _ = ?g _ _ _) => apply f_equal3 with (f := g)
- |     |-  (?g ?X ?Y ?Z _ = ?g ?X ?Y ?Z _) => apply f_equal with (f := g X Y Z)
- |     |-  (?g ?X ?Y _ _ = ?g ?X ?Y _ _) => apply f_equal2 with (f := g X Y)
- |     |-  (?g ?X _ _ _ = ?g ?X _ _ _) => apply f_equal3 with (f := g X)
- |     |-  (?g _ _ _ _ _ = ?g _ _ _ _) => apply f_equal4 with (f := g)
- end.
-
-(************************************** 
- A stupid tactic that tries auto also after applying sym_equal
-**************************************)
-
-Ltac sauto := (intros; apply sym_equal; auto; fail) || auto.