Coq.Sets.Relations_2

# Module Coq.Sets.Relations_2

``Require` `Export` Relations_1.

`Section` Relations_2.
`Variable` U: Type.
`Variable` R: (Relation U).

`Inductive` Rstar : (Relation U) :=
Rstar_0: (x: U) (Rstar x x)
| Rstar_n: (x, y, z: U) (R x y) -> (Rstar y z) -> (Rstar x z).

`Inductive` Rstar1 : (Relation U) :=
Rstar1_0: (x: U) (Rstar1 x x)
| Rstar1_1: (x: U) (y: U) (R x y) -> (Rstar1 x y)
| Rstar1_n: (x, y, z: U) (Rstar1 x y) -> (Rstar1 y z) -> (Rstar1 x z).

`Inductive` Rplus : (Relation U) :=
Rplus_0: (x, y: U) (R x y) -> (Rplus x y)
| Rplus_n: (x, y, z: U) (R x y) -> (Rplus y z) -> (Rplus x z).

`Definition` Strongly_confluent : Prop :=
(x, a, b: U) (R x a) -> (R x b) -> (exT U [z: U] (R a z) /\ (R b z)).

`End` Relations_2.

`Hints` Resolve Rstar_0 : sets v62.
`Hints` Resolve Rstar1_0 : sets v62.
`Hints` Resolve Rstar1_1 : sets v62.
`Hints` Resolve Rplus_0 : sets v62.

`

Index