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authorGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-02-14 14:39:07 +0000
committerGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-02-14 14:39:07 +0000
commit67f72c93f5f364591224a86c52727867e02a8f71 (patch)
treeecf630daf8346e77e6620233d8f3e6c18a0c9b3c /theories/Init/Wf.v
parentb239b208eb9a66037b0c629cf7ccb6e4b110636a (diff)
option -dump-glob pour coqdoc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2474 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Init/Wf.v')
-rwxr-xr-xtheories/Init/Wf.v19
1 files changed, 10 insertions, 9 deletions
diff --git a/theories/Init/Wf.v b/theories/Init/Wf.v
index 752dfbccd..58c159b78 100755
--- a/theories/Init/Wf.v
+++ b/theories/Init/Wf.v
@@ -8,22 +8,23 @@
(*i $Id$ i*)
-(* This module proves the validity of
+(** This module proves the validity of
- well-founded recursion (also called course of values)
- well-founded induction
+
from a well-founded ordering on a given set *)
Require Logic.
Require LogicSyntax.
-(* Well-founded induction principle on Prop *)
+(** Well-founded induction principle on Prop *)
Chapter Well_founded.
Variable A : Set.
Variable R : A -> A -> Prop.
- (* The accessibility predicate is defined to be non-informative *)
+ (** The accessibility predicate is defined to be non-informative *)
Inductive Acc : A -> Prop
:= Acc_intro : (x:A)((y:A)(R y x)->(Acc y))->(Acc x).
@@ -32,7 +33,7 @@ Chapter Well_founded.
NewDestruct 1; Trivial.
Defined.
- (* the informative elimination :
+ (** the informative elimination :
[let Acc_rec F = let rec wf x = F x wf in wf] *)
Section AccRec.
@@ -44,11 +45,11 @@ Chapter Well_founded.
End AccRec.
- (* A relation is well-founded if every element is accessible *)
+ (** A relation is well-founded if every element is accessible *)
Definition well_founded := (a:A)(Acc a).
- (* well-founded induction on Set and Prop *)
+ (** well-founded induction on Set and Prop *)
Hypothesis Rwf : well_founded.
@@ -64,7 +65,7 @@ Chapter Well_founded.
Intros; Apply (Acc_ind P); Auto.
Qed.
-(* Building fixpoints *)
+(** Building fixpoints *)
Section FixPoint.
@@ -76,8 +77,8 @@ Fixpoint Fix_F [x:A;r:(Acc x)] : (P x) :=
Definition fix := [x:A](Fix_F x (Rwf x)).
-(* Proof that [well_founded_induction] satisfies the fixpoint equation.
- It requires an extra property of the functional *)
+(** Proof that [well_founded_induction] satisfies the fixpoint equation.
+ It requires an extra property of the functional *)
Hypothesis F_ext :
(x:A)(f,g:(y:A)(R y x)->(P y))