## lustrec-tests / regression_tests / lustre_files / success / kind_fmcad08 / misc / durationThm_2.lus @ 2d37a1e1

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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 3: |

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-- (p -k-> q and r -k-> t) => (p and r) -k-> (q and t) |

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-- Not provable in luke-* |

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node top (k0: int; p, q, r, t : bool) returns (OK: bool); |

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--@ contract guarantees OK; |

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var k: int; |

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env : bool; |

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let |

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k = k0-> pre(k); |

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

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OK = env => ((Age(p and r)>=k) => (q and t)); |

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--%PROPERTY OK=true; |

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--%MAIN; |

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tel |