Lax Lean Archive

Triangles are maximal outerplanar

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

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    Natural Language Statement

    Theorem

    Every triangle is maximal outerplanar.

    A triangle is drawn using three explicit points on a circle. Since the triangle is complete, no further edge can be added on its existing vertices.

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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.Triangles
    2import Lax68.MaximalOuterplanar
    3
    4/-!
    5---
    6title: Triangles are maximal outerplanar
    7type: theorem
    8---
    9Every triangle is maximal outerplanar.
    10
    11A triangle is drawn using three explicit points on a circle. Since the
    12triangle is complete, no further edge can be added on its existing vertices.
    13-/
    14
    15set_option autoImplicit false
    16
    17namespace Lax68.TriangleMaximalOuterplanar
    18
    19/-- Every triangle is maximal outerplanar. -/
    20axiom triangle_maximalOuterplanar
    21 {V : Type*} {G : SimpleGraph V} :
    22 Lax68.Triangles.IsTriangle G →
    23 Lax68.MaximalOuterplanar.IsMaximalOuterplanar G
    24
    25end Lax68.TriangleMaximalOuterplanar
    26
    Show Proof
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