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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-06-08 16:13:37 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-06-08 16:13:37 +0000
commit47e5f716f7ded0eec43b00d49955d56c370c3596 (patch)
treee7fbe16925eacc72bdd9ebeb65c2a20b8bb0eef0 /theories/ZArith
parent70f8c345685278a567fbb075f222c79f0533e90e (diff)
- Extension de "generalize" en "generalize c as id at occs".
- Ajout clause "in" à "remember" (et passage du code en ML). - Ajout clause "in" à "induction"/"destruct" qui, en ce cas, ajoute aussi une égalité pour se souvenir du terme sur lequel l'induction ou l'analyse de cas s'applique. - Ajout "pose t as id" en standard (Matthieu: j'ai enlevé celui de Programs qui avait la sémantique de "pose proof" tandis que le nouveau a la même sémantique que "pose (id:=t)"). - Un peu de réorganisation, uniformisation de noms dans Arith, et ajout EqNat dans Arith. - Documentation tactiques et notations de tactiques. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11072 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith')
-rw-r--r--theories/ZArith/Zmisc.v15
-rw-r--r--theories/ZArith/Zpower.v1
2 files changed, 2 insertions, 14 deletions
diff --git a/theories/ZArith/Zmisc.v b/theories/ZArith/Zmisc.v
index b05acd730..c99582a25 100644
--- a/theories/ZArith/Zmisc.v
+++ b/theories/ZArith/Zmisc.v
@@ -8,6 +8,7 @@
(*i $Id$ i*)
+Require Import Wf_nat.
Require Import BinInt.
Require Import Zcompare.
Require Import Zorder.
@@ -18,11 +19,6 @@ Open Local Scope Z_scope.
(** Iterators *)
(** [n]th iteration of the function [f] *)
-Fixpoint iter_nat (n:nat) (A:Type) (f:A -> A) (x:A) {struct n} : A :=
- match n with
- | O => x
- | S n' => f (iter_nat n' A f x)
- end.
Fixpoint iter_pos (n:positive) (A:Type) (f:A -> A) (x:A) {struct n} : A :=
match n with
@@ -38,15 +34,6 @@ Definition iter (n:Z) (A:Type) (f:A -> A) (x:A) :=
| Zneg p => x
end.
-Theorem iter_nat_plus :
- forall (n m:nat) (A:Type) (f:A -> A) (x:A),
- iter_nat (n + m) A f x = iter_nat n A f (iter_nat m A f x).
-Proof.
- simple induction n;
- [ simpl in |- *; auto with arith
- | intros; simpl in |- *; apply f_equal with (f := f); apply H ].
-Qed.
-
Theorem iter_nat_of_P :
forall (p:positive) (A:Type) (f:A -> A) (x:A),
iter_pos p A f x = iter_nat (nat_of_P p) A f x.
diff --git a/theories/ZArith/Zpower.v b/theories/ZArith/Zpower.v
index f3f357de1..7ee8b9766 100644
--- a/theories/ZArith/Zpower.v
+++ b/theories/ZArith/Zpower.v
@@ -8,6 +8,7 @@
(*i $Id$ i*)
+Require Import Wf_nat.
Require Import ZArith_base.
Require Export Zpow_def.
Require Import Omega.