diff options
| -rw-r--r-- | theories/Logic/ClassicalChoice.v | 35 |
1 files changed, 35 insertions, 0 deletions
diff --git a/theories/Logic/ClassicalChoice.v b/theories/Logic/ClassicalChoice.v new file mode 100644 index 0000000000..b7fb6845a0 --- /dev/null +++ b/theories/Logic/ClassicalChoice.v @@ -0,0 +1,35 @@ +(***********************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *) +(* \VV/ *************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(***********************************************************************) + +(*i logic: "-strongly-classical" i*) + +(*i $Id$ i*) + +(** This file provides classical logic and functional choice *) + +(** This file extends ClassicalDescription.v with the axiom of choice. + As ClassicalDescription.v, it implies the double-negation of + excluded-middle in Set and implies a strongly classical + world. Especially it conflicts with impredicativity of Set, knowing + that true<>false in Set. + + This file and all files depending on it require option -strongly-classical +*) + +Require Export ClassicalDescription. +Require Export RelationalChoice. +Require ChoiceFacts. + +Theorem choice : + (A:Type;B:Type;R: A->B->Prop) + ((x:A)(EX y:B|(R x y))) -> (EX f:A->B | (x:A)(R x (f x))). +Proof. +Apply description_rel_choice_imp_funct_choice. +Exact description. +Exact relational_choice. +Qed. |