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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/Relations
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/Relations')
-rwxr-xr-xtheories/Relations/Newman.v14
-rwxr-xr-xtheories/Relations/Relation_Operators.v2
-rwxr-xr-xtheories/Relations/Rstar.v17
3 files changed, 16 insertions, 17 deletions
diff --git a/theories/Relations/Newman.v b/theories/Relations/Newman.v
index 2fe408543..57e93240a 100755
--- a/theories/Relations/Newman.v
+++ b/theories/Relations/Newman.v
@@ -26,12 +26,12 @@ Theorem coherence_intro : (x:A)(y:A)(z:A)(Rstar x z)->(Rstar y z)->(coherence x
Proof [x:A][y:A][z:A][h1:(Rstar x z)][h2:(Rstar y z)]
(exT_intro2 A (Rstar x) (Rstar y) z h1 h2).
-(* A very simple case of coherence : *)
+(** A very simple case of coherence : *)
Lemma Rstar_coherence : (x:A)(y:A)(Rstar x y)->(coherence x y).
Proof [x:A][y:A][h:(Rstar x y)](coherence_intro x y y h (Rstar_reflexive y)).
-(* coherence is symmetric *)
+(** coherence is symmetric *)
Lemma coherence_sym: (x:A)(y:A)(coherence x y)->(coherence y x).
Proof [x:A][y:A][h:(coherence x y)]
(exT2_ind A (Rstar x) (Rstar y) (coherence y x)
@@ -49,30 +49,30 @@ Definition noetherian :=
Section Newman_section.
-(* The general hypotheses of the theorem *)
+(** The general hypotheses of the theorem *)
Hypothesis Hyp1:noetherian.
Hypothesis Hyp2:(x:A)(local_confluence x).
-(* The induction hypothesis *)
+(** The induction hypothesis *)
Section Induct.
Variable x:A.
Hypothesis hyp_ind:(u:A)(R x u)->(confluence u).
-(* Confluence in x *)
+(** Confluence in [x] *)
Variables y,z:A.
Hypothesis h1:(Rstar x y).
Hypothesis h2:(Rstar x z).
-(* particular case x->u and u->*y *)
+(** particular case [x->u] and [u->*y] *)
Section Newman_.
Variable u:A.
Hypothesis t1:(R x u).
Hypothesis t2:(Rstar u y).
-(* In the usual diagram, we assume also x->v and v->*z *)
+(** In the usual diagram, we assume also [x->v] and [v->*z] *)
Theorem Diagram : (v:A)(u1:(R x v))(u2:(Rstar v z))(coherence y z).
diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v
index a5c81e2e3..7b07ac0db 100755
--- a/theories/Relations/Relation_Operators.v
+++ b/theories/Relations/Relation_Operators.v
@@ -20,7 +20,7 @@ Require Relation_Definitions.
Require PolyList.
Require PolyListSyntax.
-(* Some operators to build relations *)
+(** Some operators to build relations *)
Section Transitive_Closure.
Variable A: Set.
diff --git a/theories/Relations/Rstar.v b/theories/Relations/Rstar.v
index ff2e02a4b..90ab6d6c2 100755
--- a/theories/Relations/Rstar.v
+++ b/theories/Relations/Rstar.v
@@ -8,15 +8,15 @@
(*i $Id$ i*)
-(* Properties of a binary relation R on type A *)
+(** Properties of a binary relation [R] on type [A] *)
Section Rstar.
Variable A : Type.
Variable R : A->A->Prop.
-(* Definition of the reflexive-transitive closure R* of R *)
-(* Smallest reflexive P containing R o P *)
+(** Definition of the reflexive-transitive closure [R*] of [R] *)
+(** Smallest reflexive [P] containing [R o P] *)
Definition Rstar := [x,y:A](P:A->A->Prop)
((u:A)(P u u))->((u:A)(v:A)(w:A)(R u v)->(P v w)->(P u w)) -> (P x y).
@@ -32,7 +32,7 @@ Theorem Rstar_R: (x:A)(y:A)(z:A)(R x y)->(Rstar y z)->(Rstar x z).
[h1:(u:A)(P u u)][h2:(u:A)(v:A)(w:A)(R u v)->(P v w)->(P u w)]
(h2 x y z t1 (t2 P h1 h2)).
-(* We conclude with transitivity of Rstar : *)
+(** We conclude with transitivity of [Rstar] : *)
Theorem Rstar_transitive: (x:A)(y:A)(z:A)(Rstar x y)->(Rstar y z)->(Rstar x z).
Proof [x:A][y:A][z:A][h:(Rstar x y)]
@@ -41,8 +41,8 @@ Theorem Rstar_transitive: (x:A)(y:A)(z:A)(Rstar x y)->(Rstar y z)->(Rstar x z)
([u:A][v:A][w:A][t1:(R u v)][t2:(Rstar w z)->(Rstar v z)]
[t3:(Rstar w z)](Rstar_R u v z t1 (t2 t3)))).
-(* Another characterization of R* *)
-(* Smallest reflexive P containing R o R* *)
+(** Another characterization of [R*] *)
+(** Smallest reflexive [P] containing [R o R*] *)
Definition Rstar' := [x:A][y:A](P:A->A->Prop)
((P x x))->((u:A)(R x u)->(Rstar u y)->(P x y)) -> (P x y).
@@ -55,7 +55,7 @@ Theorem Rstar'_R: (x:A)(y:A)(z:A)(R x z)->(Rstar z y)->(Rstar' x y).
[P:A->A->Prop][h1:(P x x)]
[h2:(u:A)(R x u)->(Rstar u y)->(P x y)](h2 z t1 t2).
-(* Equivalence of the two definitions: *)
+(** Equivalence of the two definitions: *)
Theorem Rstar'_Rstar: (x:A)(y:A)(Rstar' x y)->(Rstar x y).
Proof [x:A][y:A][h:(Rstar' x y)]
@@ -67,8 +67,7 @@ Theorem Rstar_Rstar': (x:A)(y:A)(Rstar x y)->(Rstar' x y).
(Rstar'_R u w v h1 (Rstar'_Rstar v w h2)))).
-
-(* Property of Commutativity of two relations *)
+(** Property of Commutativity of two relations *)
Definition commut := [A:Set][R1,R2:A->A->Prop]
(x,y:A)(R1 y x)->(z:A)(R2 z y)