diff options
| -rw-r--r-- | theories/Logic/ClassicalChoice.v | 9 | ||||
| -rw-r--r-- | theories/Logic/Diaconescu.v | 8 |
2 files changed, 9 insertions, 8 deletions
diff --git a/theories/Logic/ClassicalChoice.v b/theories/Logic/ClassicalChoice.v index 0bc491e204..69887a540a 100644 --- a/theories/Logic/ClassicalChoice.v +++ b/theories/Logic/ClassicalChoice.v @@ -23,10 +23,11 @@ Require Import ChoiceFacts. Theorem choice : forall (A B:Type) (R:A -> B -> Prop), - (forall x:A, exists y : B, R x y) -> + (forall x:A, exists y : B, R x y) -> exists f : A -> B, (forall x:A, R x (f x)). Proof. +intros A B. apply description_rel_choice_imp_funct_choice. -exact description. -exact relational_choice. -Qed.
\ No newline at end of file +exact (description A B). +exact (relational_choice A B). +Qed. diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v index d815b9dda7..5f7112fd7d 100644 --- a/theories/Logic/Diaconescu.v +++ b/theories/Logic/Diaconescu.v @@ -59,18 +59,18 @@ Qed. Require Import ChoiceFacts. -Variable rel_choice : RelationalChoice. +Variable rel_choice : forall A B:Type, RelationalChoice A B. Lemma guarded_rel_choice : forall (A B:Type) (P:A -> Prop) (R:A -> B -> Prop), (forall x:A, P x -> exists y : B, R x y) -> - exists R' : A -> B -> Prop, + exists R' : A -> B -> Prop, (forall x:A, P x -> exists y : B, R x y /\ R' x y /\ (forall y':B, R' x y' -> y = y')). Proof. - exact - (rel_choice_and_proof_irrel_imp_guarded_rel_choice rel_choice proof_irrel). + apply + (rel_choice_and_proof_irrel_imp_guarded_rel_choice rel_choice proof_irrel). Qed. (** The form of choice we need: there is a functional relation which chooses |