diff options
Diffstat (limited to 'theories/Logic/Epsilon.v')
| -rw-r--r-- | theories/Logic/Epsilon.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Logic/Epsilon.v b/theories/Logic/Epsilon.v index 65d4d853..d433be94 100644 --- a/theories/Logic/Epsilon.v +++ b/theories/Logic/Epsilon.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Epsilon.v 10170 2007-10-03 14:41:25Z herbelin $ i*) +(*i $Id$ i*) (** This file provides indefinite description under the form of Hilbert's epsilon operator; it does not assume classical logic. *) @@ -17,12 +17,12 @@ Set Implicit Arguments. (** Hilbert's epsilon: operator and specification in one statement *) -Axiom epsilon_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), + forall (A : Type) (P : A->Prop), (exists x, P x) -> { x : A | P x }. Proof. apply epsilon_imp_constructive_indefinite_description. @@ -45,7 +45,7 @@ Proof. Qed. Lemma constructive_definite_description : - forall (A : Type) (P : A->Prop), + forall (A : Type) (P : A->Prop), (exists! x, P x) -> { x : A | P x }. Proof. apply iota_imp_constructive_definite_description. @@ -57,7 +57,7 @@ Qed. Definition epsilon (A : Type) (i:inhabited A) (P : A->Prop) : A := proj1_sig (epsilon_statement P i). -Definition epsilon_spec (A : Type) (i:inhabited A) (P : A->Prop) : +Definition epsilon_spec (A : Type) (i:inhabited A) (P : A->Prop) : (exists x, P x) -> P (epsilon i P) := proj2_sig (epsilon_statement P i). @@ -66,7 +66,7 @@ Definition epsilon_spec (A : Type) (i:inhabited A) (P : A->Prop) : Definition iota (A : Type) (i:inhabited A) (P : A->Prop) : A := proj1_sig (iota_statement P i). -Definition iota_spec (A : Type) (i:inhabited A) (P : A->Prop) : +Definition iota_spec (A : Type) (i:inhabited A) (P : A->Prop) : (exists! x:A, P x) -> P (iota i P) := proj2_sig (iota_statement P i). |