Library Coq.Logic.PropExtensionalityFacts
Some facts and definitions about propositional and predicate extensionality
 
We investigate the relations between the following extensionality principles
 
 
Table of contents
 
1. Definitions
 
2.1 Predicate extensionality <-> Proposition extensionality + Propositional functional extensionality
 
2.2 Propositional extensionality -> Provable propositional extensionality
 
2.3 Propositional extensionality -> Refutable propositional extensionality
 
- Proposition extensionality
- Predicate extensionality
- Propositional functional extensionality
- Provable-proposition extensionality
- Refutable-proposition extensionality
- Extensional proposition representatives
- Extensional predicate representatives
- Extensional propositional function representatives
Set Implicit Arguments.
Provable-proposition extensionality 
Refutable-proposition extensionality 
Predicate extensionality 
Propositional functional extensionality 
Propositional and predicate extensionality
Predicate extensionality <-> Propositional extensionality + Propositional functional extensionality
Lemma PredExt_imp_PropExt : PredicateExtensionality -> PropositionalExtensionality.
Lemma PredExt_imp_PropFunExt : PredicateExtensionality -> PropositionalFunctionalExtensionality.
Lemma PropExt_and_PropFunExt_imp_PredExt :
PropositionalExtensionality -> PropositionalFunctionalExtensionality -> PredicateExtensionality.
Theorem PropExt_and_PropFunExt_iff_PredExt :
PropositionalExtensionality /\ PropositionalFunctionalExtensionality <-> PredicateExtensionality.
