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Integral start times suffice

Lax391470.IntegralStartTimes · concepts/Lax391470/IntegralStartTimes.lean · lax-391470

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    Natural Language Statement

    Theorem

    An instance has a feasible schedule with real start times if and only if it has one with integer start times. Rounding every start time up to the next integer preserves feasibility, because release times, deadlines and processing times are integers.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    Lean source view on GitHub

    1import Lax391470.Scheduling
    2
    3/-!
    4---
    5title: Integral start times suffice
    6type: theorem
    7---
    8An instance has a feasible schedule with real start times if and only if it has one with
    9integer start times. Rounding every start time up to the next integer preserves
    10feasibility, because release times, deadlines and processing times are integers.
    11
    12# Formalization notes
    13
    14The source defines a schedule as a real-valued assignment of start times and remarks
    15that, by discretization, start times can always be taken to be integers. This statement
    16is that remark. It is what licenses the rest of the submission to define feasibility over
    17the integers.
    18-/
    19
    20namespace Lax391470.IntegralStartTimes
    21
    22open Lax391470.Scheduling
    23
    24/-- Real and integer start times decide the same instances. -/
    25axiom realSchedulable_iff (I : Instance) : I.RealSchedulable ↔ I.Schedulable
    26
    27end Lax391470.IntegralStartTimes
    28
    Show Proof
    Formalization notes

    The source defines a schedule as a real-valued assignment of start times and remarks that, by discretization, start times can always be taken to be integers. This statement is that remark. It is what licenses the rest of the submission to define feasibility over the integers.

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