diff options
Diffstat (limited to 'theories/Sets')
-rwxr-xr-x | theories/Sets/Relations_2.v | 24 | ||||
-rwxr-xr-x | theories/Sets/Relations_3.v | 4 |
2 files changed, 14 insertions, 14 deletions
diff --git a/theories/Sets/Relations_2.v b/theories/Sets/Relations_2.v index 918e45ee1..11ac85e84 100755 --- a/theories/Sets/Relations_2.v +++ b/theories/Sets/Relations_2.v @@ -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 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 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 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 (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 (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). diff --git a/theories/Sets/Relations_3.v b/theories/Sets/Relations_3.v index d6202cffe..ec8fb7e6d 100755 --- a/theories/Sets/Relations_3.v +++ b/theories/Sets/Relations_3.v @@ -46,9 +46,9 @@ Section Relations_3. Definition Confluent : Prop := forall x:U, confluent x. - Inductive noetherian : U -> Prop := + Inductive noetherian (x: U) : Prop := definition_of_noetherian : - forall x:U, (forall y:U, R x y -> noetherian y) -> noetherian x. + (forall y:U, R x y -> noetherian y) -> noetherian x. Definition Noetherian : Prop := forall x:U, noetherian x. |