# Package relation-well-founded-def: Definition of well-founded relations

## Information

name | relation-well-founded-def |

version | 1.36 |

description | Definition of well-founded relations |

author | Joe Leslie-Hurd <joe@gilith.com> |

license | HOLLight |

provenance | HOL Light theory extracted on 2012-12-02 |

requires | bool |

show | Data.Bool Relation |

## Files

- Package tarball relation-well-founded-def-1.36.tgz
- Theory source file relation-well-founded-def.thy (included in the package tarball)

## Defined Constant

- Relation
- wellFounded

## Theorem

⊦ ∀r. wellFounded r ⇔ ∀p. (∃x. p x) ⇒ ∃x. p x ∧ ∀y. r y x ⇒ ¬p y

## External Type Operators

- →
- bool

## External Constants

- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- ⊤

- Bool

## Assumptions

⊦ ⊤

⊦ (∀) = λp. p = λx. ⊤