summaryrefslogtreecommitdiff
path: root/theories/Arith/Wf_nat.v
diff options
context:
space:
mode:
authorGravatar Stephane Glondu <steph@glondu.net>2012-01-12 16:04:54 +0100
committerGravatar Stephane Glondu <steph@glondu.net>2012-01-12 16:04:54 +0100
commit39efc41237ec906226a3a53d7396d51173495204 (patch)
tree87cd58d72d43469d2a2a0a127c1060d7c9e0206b /theories/Arith/Wf_nat.v
parent5fe4ac437bed43547b3695664974f492b55cb553 (diff)
parent97fefe1fcca363a1317e066e7f4b99b9c1e9987b (diff)
Remove non-DFSG contentsupstream/8.4_beta+dfsg
Diffstat (limited to 'theories/Arith/Wf_nat.v')
-rw-r--r--theories/Arith/Wf_nat.v23
1 files changed, 4 insertions, 19 deletions
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v
index 23419531..b4468dd1 100644
--- a/theories/Arith/Wf_nat.v
+++ b/theories/Arith/Wf_nat.v
@@ -1,13 +1,11 @@
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *)
+(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: Wf_nat.v 14641 2011-11-06 11:59:10Z herbelin $ i*)
-
(** Well-founded relations and natural numbers *)
Require Import Lt.
@@ -260,19 +258,6 @@ Qed.
Unset Implicit Arguments.
-(** [n]th iteration of the function [f] *)
-
-Fixpoint iter_nat (n:nat) (A:Type) (f:A -> A) (x:A) : A :=
- match n with
- | O => x
- | S n' => f (iter_nat n' A f 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.
+Notation iter_nat := @nat_iter (only parsing).
+Notation iter_nat_plus := @nat_iter_plus (only parsing).
+Notation iter_nat_invariant := @nat_iter_invariant (only parsing).