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