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src/Sequents/T.thy

changeset 51309 | 473303ef6e34 |

parent 42814 | 5af15f1e2ef6 |

child 54742 | 7a86358a3c0b |

equal
deleted
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51308:51e158e988a5 | 51309:473303ef6e34 |
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5 |
5 |

6 theory T |
6 theory T |

7 imports Modal0 |
7 imports Modal0 |

8 begin |
8 begin |

9 |
9 |

10 axioms |
10 axiomatization where |

11 (* Definition of the star operation using a set of Horn clauses *) |
11 (* Definition of the star operation using a set of Horn clauses *) |

12 (* For system T: gamma * == {P | []P : gamma} *) |
12 (* For system T: gamma * == {P | []P : gamma} *) |

13 (* delta * == {P | <>P : delta} *) |
13 (* delta * == {P | <>P : delta} *) |

14 |
14 |

15 lstar0: "|L>" |
15 lstar0: "|L>" and |

16 lstar1: "$G |L> $H ==> []P, $G |L> P, $H" |
16 lstar1: "$G |L> $H ==> []P, $G |L> P, $H" and |

17 lstar2: "$G |L> $H ==> P, $G |L> $H" |
17 lstar2: "$G |L> $H ==> P, $G |L> $H" and |

18 rstar0: "|R>" |
18 rstar0: "|R>" and |

19 rstar1: "$G |R> $H ==> <>P, $G |R> P, $H" |
19 rstar1: "$G |R> $H ==> <>P, $G |R> P, $H" and |

20 rstar2: "$G |R> $H ==> P, $G |R> $H" |
20 rstar2: "$G |R> $H ==> P, $G |R> $H" and |

21 |
21 |

22 (* Rules for [] and <> *) |
22 (* Rules for [] and <> *) |

23 |
23 |

24 boxR: |
24 boxR: |

25 "[| $E |L> $E'; $F |R> $F'; $G |R> $G'; |
25 "[| $E |L> $E'; $F |R> $F'; $G |R> $G'; |

26 $E' |- $F', P, $G'|] ==> $E |- $F, []P, $G" |
26 $E' |- $F', P, $G'|] ==> $E |- $F, []P, $G" and |

27 boxL: "$E, P, $F |- $G ==> $E, []P, $F |- $G" |
27 boxL: "$E, P, $F |- $G ==> $E, []P, $F |- $G" and |

28 diaR: "$E |- $F, P, $G ==> $E |- $F, <>P, $G" |
28 diaR: "$E |- $F, P, $G ==> $E |- $F, <>P, $G" and |

29 diaL: |
29 diaL: |

30 "[| $E |L> $E'; $F |L> $F'; $G |R> $G'; |
30 "[| $E |L> $E'; $F |L> $F'; $G |R> $G'; |

31 $E', P, $F'|- $G'|] ==> $E, <>P, $F |- $G" |
31 $E', P, $F'|- $G'|] ==> $E, <>P, $F |- $G" |

32 |
32 |

33 ML {* |
33 ML {* |