Lax Lean Archive

The Word Table Encodes the Same Graph

Lax920634.WordEncodingCorrectness · concepts/Lax920634/WordEncodingCorrectness.lean · lax-920634

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    Natural Language Statement

    Lemma

    The word table contains exactly one header and one endpoint per vertex. Its header is the graph order, every endpoint is a valid vertex label, and decoding produces exactly the specified subcubic graph.

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

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax920634.WordEncoding
    2
    3/-!
    4---
    5title: The Word Table Encodes the Same Graph
    6type: lemma
    7---
    8The word table contains exactly one header and one endpoint per vertex.
    9Its header is the graph order, every endpoint is a valid vertex label,
    10and decoding produces exactly the specified subcubic graph.
    11-/
    12
    13namespace Lax920634.WordEncodingCorrectness
    14
    15open ZigZagConstruction WordEncoding
    16
    17/-- The linear-size word encoding is complete, bounded, and faithful to the original graph. -/
    18axiom table_correct (k : ℕ) :
    19 (table k).head? = some (order k) ∧
    20 (table k).length = order k + 1 ∧
    21 (∀ j < order k,
    22 ((table k).tail[j]?).getD 0 < order k) ∧
    23 decode (order k) (table k) = graph k
    24
    25end Lax920634.WordEncodingCorrectness
    26
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