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Lax307052.PolyBounds

Constructing polynomial space bounds

concepts/Lax307052/PolyBounds.lean · lax-307052

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    Lemma

    For every polynomial pp with natural coefficients, the positive bound p(n)+n+2p(n)+n+2 is fully space-constructible. Nested input counters append the polynomial terms to a unary output track. A final scan halts at the required work position.

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    1import Lax307052.SpaceConstructibility
    2
    3/-!
    4---
    5title: Constructing polynomial space bounds
    6type: lemma
    7---
    8For every polynomial pp with natural coefficients, the positive bound
    9p(n)+n+2p(n)+n+2 is fully space-constructible.
    10Nested input counters append the polynomial terms to a unary output track.
    11A final scan halts at the required work position.
    12-/
    13
    14namespace Lax307052.PolyBounds
    15
    16open SpaceConstructibility
    17
    18axiom polynomial_constructible (p : Polynomial ℕ) :
    19 Constructible (fun n => p.eval n + n + 2)
    20
    21end Lax307052.PolyBounds
    22
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