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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/Logic/Eqdep_dec.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/Logic/Eqdep_dec.v')
-rw-r--r--theories/Logic/Eqdep_dec.v13
1 files changed, 7 insertions, 6 deletions
diff --git a/theories/Logic/Eqdep_dec.v b/theories/Logic/Eqdep_dec.v
index 96c8f91c9..68b0fcbf8 100644
--- a/theories/Logic/Eqdep_dec.v
+++ b/theories/Logic/Eqdep_dec.v
@@ -8,24 +8,25 @@
(*i $Id$ i*)
-(* We prove that there is only one proof of [x=x], i.e [(refl_equal ? x)].
+(** We prove that there is only one proof of [x=x], i.e [(refl_equal ? x)].
This holds if the equality upon the set of [x] is decidable.
A corollary of this theorem is the equality of the right projections
of two equal dependent pairs.
- Author: Thomas Kleymann \verb!<tms@dcs.ed.ac.uk>! in Lego
+ Author: Thomas Kleymann |<tms@dcs.ed.ac.uk>| in Lego
adapted to Coq by B. Barras
+
Credit: Proofs up to [K_dec] follows an outline by Michael Hedberg
*)
-(* We need some dependent elimination schemes *)
+(** We need some dependent elimination schemes *)
Set Implicit Arguments.
Require Elimdep.
- (* Bijection between [eq] and [eqT] *)
+ (** Bijection between [eq] and [eqT] *)
Definition eq2eqT: (A:Set)(x,y:A)x=y->x==y :=
[A,x,_,eqxy]<[y:A]x==y>Cases eqxy of refl_equal => (refl_eqT ? x) end.
@@ -107,7 +108,7 @@ Trivial.
Save.
- (* The corollary *)
+ (** The corollary *)
Local proj: (P:A->Prop)(ExT P)->(P x)->(P x) :=
[P,exP,def]Cases exP of
@@ -137,7 +138,7 @@ Save.
End DecidableEqDep.
- (* We deduce the K axiom for (decidable) Set *)
+ (** We deduce the [K] axiom for (decidable) Set *)
Theorem K_dec_set: (A:Set)((x,y:A){x=y}+{~x=y})
->(x:A)(P: x=x->Prop)(P (refl_equal ? x))
->(p:x=x)(P p).