## lustrec / test / src / kind_fmcad08 / misc / durationThm_1.lus @ 65f71d05

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-- Source: Bertrand Jeannet |

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-- |

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node Sofar( X : bool ) returns ( Sofar : bool ); |

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let |

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Sofar = X -> X and pre Sofar; |

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tel |

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node Age (p: bool) returns (age_of_p: int); |

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-- how long has p been maintained true in the strict past |

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let |

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age_of_p = 0 -> if pre(p) then pre(age_of_p) + 1 else 0; |

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tel |

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-- Theorem 1: |

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-- (p -k-> q and q -m-> r) => p -k+m-> r |

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-- Not provable in luke-* |

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--@ ensures OK; |

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node top (ik, im: int; p, q, r : bool) returns (OK: bool); |

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var k,m : int; |

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env : bool; |

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let |

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k = ik -> pre k; |

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m = im -> pre m; |

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env = Sofar((k>=1 and m>=1) and (Age(p)>=k => q) and (Age(q)>=m => r)); |

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OK = env => (true -> ( (Age(p)>=k+m) => r )); |

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--%PROPERTY OK=true; |

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--%MAIN; |

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tel |