diff options
Diffstat (limited to 'theories/Sets/Powerset_Classical_facts.v')
-rwxr-xr-x | theories/Sets/Powerset_Classical_facts.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Sets/Powerset_Classical_facts.v b/theories/Sets/Powerset_Classical_facts.v index 988bbd25a..71ec5b078 100755 --- a/theories/Sets/Powerset_Classical_facts.v +++ b/theories/Sets/Powerset_Classical_facts.v @@ -177,7 +177,7 @@ Qed. Lemma Included_Add : forall (X A:Ensemble U) (x:U), Included U X (Add U A x) -> - Included U X A \/ ( exists A' : _ | X = Add U A' x /\ Included U A' A). + Included U X A \/ (exists A' : _, X = Add U A' x /\ Included U A' A). Proof. intros X A x H'0; try assumption. elim (classic (In U X x)). @@ -267,7 +267,7 @@ Theorem covers_Add : Included U a A -> Included U a' A -> covers (Ensemble U) (Power_set_PO U A) a' a -> - exists x : _ | a' = Add U a x /\ In U A x /\ ~ In U a x. + exists x : _, a' = Add U a x /\ In U A x /\ ~ In U a x. Proof. intros A a a' H' H'0 H'1; try assumption. elim (setcover_inv A a a'); auto with sets. @@ -299,7 +299,7 @@ Theorem covers_is_Add : Included U a A -> Included U a' A -> (covers (Ensemble U) (Power_set_PO U A) a' a <-> - ( exists x : _ | a' = Add U a x /\ In U A x /\ ~ In U a x)). + (exists x : _, a' = Add U a x /\ In U A x /\ ~ In U a x)). Proof. intros A a a' H' H'0; split; intro K. apply covers_Add with (A := A); auto with sets. |