Lax Lean Archive

Triangulations of planar graphs are planar

Lax68.TriangulationPlanar · concepts/Lax68/TriangulationPlanar.lean · lax-68

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    Natural Language Statement

    Theorem

    If T is a triangulation of a planar graph G, then T is planar.

    Concept map
    5 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    Lean source view on GitHub

    1import Lax68.Triangulations
    2import Lax68.Planar
    3
    4/-!
    5---
    6title: Triangulations of planar graphs are planar
    7type: theorem
    8---
    9If T is a triangulation of a planar graph G, then T is planar.
    10-/
    11
    12set_option autoImplicit false
    13
    14namespace Lax68.TriangulationPlanar
    15
    16/-- If T is a triangulation of a planar graph G, then T is planar. -/
    17axiom triangulationOf_planar {V : Type*}
    18 {G T : SimpleGraph V} :
    19 Lax68.Planar.IsPlanar G →
    20 Lax68.Triangulations.IsTriangulationOf G T →
    21 Lax68.Planar.IsPlanar T
    22
    23end Lax68.TriangulationPlanar
    24
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