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| author |  herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2004-08-01 09:27:26 +0000 |
|---|---|---|
| committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2004-08-01 09:27:26 +0000 |
| commit | d846ae7e7e0a0e9e4e4343f1a4a3efb08a25d40b (patch) | |
| tree | 0349ff096406c23b98917b2985c8f43e0a205905 /theories/Logic/Diaconescu.v | |
| parent | 44074272d177ff5828a3027e26121681aad952ae (diff) | |
Commentaires coqdoc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@6001 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/Diaconescu.v')
| -rw-r--r-- | theories/Logic/Diaconescu.v | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v index 095e53caa..73a2f3e9b 100644 --- a/theories/Logic/Diaconescu.v +++ b/theories/Logic/Diaconescu.v @@ -8,7 +8,7 @@ (*i $Id$ i*) -(* R. Diaconescu [Diaconescu] showed that the Axiom of Choice in Set Theory +(** R. Diaconescu [Diaconescu] showed that the Axiom of Choice in Set Theory entails Excluded-Middle; S. Lacas and B. Werner [LacasWerner] adapted the proof to show that the axiom of choice in equivalence classes entails Excluded-Middle in Type Theory. @@ -27,12 +27,12 @@ Section PredExt_GuardRelChoice_imp_EM. -(* The axiom of extensionality for predicates *) +(** The axiom of extensionality for predicates *) Definition PredicateExtensionality := forall P Q:bool -> Prop, (forall b:bool, P b <-> Q b) -> P = Q. -(* From predicate extensionality we get propositional extensionality +(** From predicate extensionality we get propositional extensionality hence proof-irrelevance *) Require Import ClassicalFacts. @@ -54,7 +54,7 @@ Proof. apply (ext_prop_dep_proof_irrel_cic prop_ext). Qed. -(* From proof-irrelevance and relational choice, we get guarded +(** From proof-irrelevance and relational choice, we get guarded relational choice *) Require Import ChoiceFacts. @@ -73,8 +73,8 @@ Proof. (rel_choice_and_proof_irrel_imp_guarded_rel_choice rel_choice proof_irrel). Qed. -(* The form of choice we need: there is a functional relation which chooses - an element in any non empty subset of bool *) +(** The form of choice we need: there is a functional relation which chooses + an element in any non empty subset of bool *) Require Import Bool. @@ -90,8 +90,8 @@ Proof. exact (fun _ H => H). Qed. -(* The proof of the excluded middle *) -(* Remark: P could have been in Set or Type *) +(** The proof of the excluded middle *) +(** Remark: P could have been in Set or Type *) Theorem pred_ext_and_rel_choice_imp_EM : forall P:Prop, P \/ ~ P. Proof. |