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authorGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
committerGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
commit61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch)
tree961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Logic/Epsilon.v
parent6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (diff)
Delete trailing whitespaces in all *.{v,ml*} files
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/Epsilon.v')
-rw-r--r--theories/Logic/Epsilon.v10
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Logic/Epsilon.v b/theories/Logic/Epsilon.v
index ead91c9ec..d433be944 100644
--- a/theories/Logic/Epsilon.v
+++ b/theories/Logic/Epsilon.v
@@ -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).