diff options
Diffstat (limited to 'theories/Sets/Relations_2_facts.v')
| -rwxr-xr-x | theories/Sets/Relations_2_facts.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Sets/Relations_2_facts.v b/theories/Sets/Relations_2_facts.v index 4fda8d8e9..2a0aaf98b 100755 --- a/theories/Sets/Relations_2_facts.v +++ b/theories/Sets/Relations_2_facts.v @@ -67,7 +67,7 @@ Qed. Theorem Rstar_cases : forall (U:Type) (R:Relation U) (x y:U), - Rstar U R x y -> x = y \/ ( exists u : _ | R x u /\ Rstar U R u y). + Rstar U R x y -> x = y \/ (exists u : _, R x u /\ Rstar U R u y). Proof. intros U R x y H'; elim H'; auto with sets. intros x0 y0 z H'0 H'1 H'2; right; exists y0; auto with sets. @@ -116,7 +116,7 @@ Qed. Theorem RstarRplus_RRstar : forall (U:Type) (R:Relation U) (x y z:U), - Rstar U R x y -> Rplus U R y z -> exists u : _ | R x u /\ Rstar U R u z. + Rstar U R x y -> Rplus U R y z -> exists u : _, R x u /\ Rstar U R u z. Proof. generalize Rstar_contains_Rplus; intro T; red in T. generalize Rstar_transitive; intro T1; red in T1. @@ -134,7 +134,7 @@ Theorem Lemma1 : Strongly_confluent U R -> forall x b:U, Rstar U R x b -> - forall a:U, R x a -> exists z : _ | Rstar U R a z /\ R b z. + forall a:U, R x a -> exists z : _, Rstar U R a z /\ R b z. Proof. intros U R H' x b H'0; elim H'0. intros x0 a H'1; exists a; auto with sets. |