Library Coq.Logic.Epsilon
This file provides indefinite description under the form of
Hilbert's epsilon operator; it does not assume classical logic.
Hilbert's epsilon: operator and specification in one statement
Axiom epsilon_statement :
forall (
A :
Type) (
P :
A->Prop),
inhabited A ->
{
x :
A | (
exists x,
P x) ->
P x }.
Lemma constructive_indefinite_description :
forall (
A :
Type) (
P :
A->Prop),
(
exists x,
P x) -> {
x :
A |
P x }.
Lemma small_drinkers'_paradox :
forall (
A:Type) (
P:A ->
Prop),
inhabited A ->
exists x, (
exists x,
P x) ->
P x.
Theorem iota_statement :
forall (
A :
Type) (
P :
A->Prop),
inhabited A ->
{
x :
A | (
exists!
x :
A,
P x) ->
P x }.
Lemma constructive_definite_description :
forall (
A :
Type) (
P :
A->Prop),
(
exists!
x,
P x) -> {
x :
A |
P x }.
Hilbert's epsilon operator and its specification
Church's iota operator and its specification