diff options
Diffstat (limited to 'theories/Sets/Relations_2.v')
| -rw-r--r--[-rwxr-xr-x] | theories/Sets/Relations_2.v | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/theories/Sets/Relations_2.v b/theories/Sets/Relations_2.v index 15d3ee2d..a74102fd 100755..100644 --- a/theories/Sets/Relations_2.v +++ b/theories/Sets/Relations_2.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Relations_2.v,v 1.4.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Relations_2.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Relations_1. @@ -32,18 +32,18 @@ Section Relations_2. Variable U : Type. Variable R : Relation U. -Inductive Rstar : Relation U := - | Rstar_0 : forall x:U, Rstar x x - | Rstar_n : forall x y z:U, R x y -> Rstar y z -> Rstar x z. +Inductive Rstar (x:U) : U -> Prop := + | Rstar_0 : Rstar x x + | Rstar_n : forall y z:U, R x y -> Rstar y z -> Rstar x z. -Inductive Rstar1 : Relation U := - | Rstar1_0 : forall x:U, Rstar1 x x - | Rstar1_1 : forall x y:U, R x y -> Rstar1 x y - | Rstar1_n : forall x y z:U, Rstar1 x y -> Rstar1 y z -> Rstar1 x z. +Inductive Rstar1 (x:U) : U -> Prop := + | Rstar1_0 : Rstar1 x x + | Rstar1_1 : forall y:U, R x y -> Rstar1 x y + | Rstar1_n : forall y z:U, Rstar1 x y -> Rstar1 y z -> Rstar1 x z. -Inductive Rplus : Relation U := - | Rplus_0 : forall x y:U, R x y -> Rplus x y - | Rplus_n : forall x y z:U, R x y -> Rplus y z -> Rplus x z. +Inductive Rplus (x:U) : U -> Prop := + | Rplus_0 : forall y:U, R x y -> Rplus x y + | Rplus_n : forall y z:U, R x y -> Rplus y z -> Rplus x z. Definition Strongly_confluent : Prop := forall x a b:U, R x a -> R x b -> ex (fun z:U => R a z /\ R b z). |