diff options
Diffstat (limited to 'theories/Logic/ClassicalDescription.v')
| -rw-r--r-- | theories/Logic/ClassicalDescription.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Logic/ClassicalDescription.v b/theories/Logic/ClassicalDescription.v index 26e696a7cd..a20036f0a5 100644 --- a/theories/Logic/ClassicalDescription.v +++ b/theories/Logic/ClassicalDescription.v @@ -26,15 +26,15 @@ Axiom dependent_description : forall (A:Type) (B:A -> Type) (R:forall x:A, B x -> Prop), (forall x:A, - exists y : B x | R x y /\ (forall y':B x, R x y' -> y = y')) -> - exists f : forall x:A, B x | (forall x:A, R x (f x)). + exists y : B x, R x y /\ (forall y':B x, R x y' -> y = y')) -> + exists f : forall x:A, B x, (forall x:A, R x (f x)). (** Principle of definite description (aka axiom of unique choice) *) Theorem description : forall (A B:Type) (R:A -> B -> Prop), - (forall x:A, exists y : B | R x y /\ (forall y':B, R x y' -> y = y')) -> - exists f : A -> B | (forall x:A, R x (f x)). + (forall x:A, exists y : B, R x y /\ (forall y':B, R x y' -> y = y')) -> + exists f : A -> B, (forall x:A, R x (f x)). Proof. intros A B. apply (dependent_description A (fun _ => B)). @@ -46,7 +46,7 @@ Theorem classic_set : ((forall P:Prop, {P} + {~ P}) -> False) -> False. Proof. intro HnotEM. pose (R := fun A b => A /\ true = b \/ ~ A /\ false = b). -assert (H : exists f : Prop -> bool | (forall A:Prop, R A (f A))). +assert (H : exists f : Prop -> bool, (forall A:Prop, R A (f A))). apply description. intro A. destruct (classic A) as [Ha| Hnota]. |