## lustrec / test / src / kind_fmcad08 / misc / durationThm_2.lus @ 0cbf0839

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1 | 0cbf0839 | ploc | -- |
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2 | -- Source: Bertrand Jeannet |
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3 | -- |
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4 | |||

5 | node Sofar( X : bool ) returns ( Sofar : bool ); |
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6 | let |
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7 | Sofar = X -> X and pre Sofar; |
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8 | tel |
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9 | |||

10 | |||

11 | node Age (p: bool) returns (age_of_p: int); |
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12 | -- how long has p been maintained true in the strict past |
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13 | let |
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14 | age_of_p = 0 -> if pre(p) then pre(age_of_p) + 1 else 0; |
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15 | tel |
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16 | |||

17 | -- Theorem 3: |
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18 | -- (p -k-> q and r -k-> t) => (p and r) -k-> (q and t) |
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19 | |||

20 | -- Not provable in luke-* |
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21 | node top (k0: int; p, q, r, t : bool) returns (OK: bool); |
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22 | var k: int; |
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23 | env : bool; |
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24 | let |
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25 | k = k0-> pre(k); |
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26 | env = Sofar((k>=1) and (Age(p)>=k => q) and (Age(r)>=k => t)); |
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27 | OK = env => ((Age(p and r)>=k) => (q and t)); |
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28 | --%PROPERTY OK=true; |
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29 | --%MAIN; |
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30 | tel |