diff options
Diffstat (limited to 'theories/Logic/Diaconescu.v')
-rw-r--r-- | theories/Logic/Diaconescu.v | 19 |
1 files changed, 12 insertions, 7 deletions
diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v index c124e7141..3317766c9 100644 --- a/theories/Logic/Diaconescu.v +++ b/theories/Logic/Diaconescu.v @@ -1,10 +1,12 @@ (* -*- coding: utf-8 -*- *) (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) (* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) (************************************************************************) (** Diaconescu showed that the Axiom of Choice entails Excluded-Middle @@ -40,6 +42,7 @@ [[Carlström04]] Jesper Carlström, EM + Ext_ + AC_int is equivalent to AC_ext, Mathematical Logic Quaterly, vol 50(3), pp 236-240, 2004. *) +Require ClassicalFacts ChoiceFacts. (**********************************************************************) (** * Pred. Ext. + Rel. Axiom of Choice -> Excluded-Middle *) @@ -54,7 +57,7 @@ Definition PredicateExtensionality := (** From predicate extensionality we get propositional extensionality hence proof-irrelevance *) -Require Import ClassicalFacts. +Import ClassicalFacts. Variable pred_extensionality : PredicateExtensionality. @@ -76,7 +79,7 @@ Qed. (** From proof-irrelevance and relational choice, we get guarded relational choice *) -Require Import ChoiceFacts. +Import ChoiceFacts. Variable rel_choice : RelationalChoice. @@ -89,7 +92,7 @@ Qed. (** 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. +Import Bool. Lemma AC_bool_subset_to_bool : exists R : (bool -> Prop) -> bool -> Prop, @@ -161,6 +164,8 @@ End PredExt_RelChoice_imp_EM. Section ProofIrrel_RelChoice_imp_EqEM. +Import ChoiceFacts. + Variable rel_choice : RelationalChoice. Variable proof_irrelevance : forall P:Prop , forall x y:P, x=y. |