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Incomparability is symmetric and irreflexive

Lax825442.IncomparableProperties · concepts/Lax825442/IncomparableProperties.lean · lax-825442

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    Natural Language Statement

    Theorem

    Incomparability of graph parameters is symmetric: exchanging the parameters exchanges its two nonbounds. It is also irreflexive, since every parameter bounds itself using the identity function.

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    Lean source view on GitHub

    1import Lax825442.Incomparable
    2
    3/-!
    4---
    5title: Incomparability is symmetric and irreflexive
    6type: theorem
    7---
    8Incomparability of graph parameters is symmetric: exchanging the parameters
    9exchanges its two nonbounds. It is also irreflexive, since every parameter
    10bounds itself using the identity function.
    11-/
    12
    13namespace Lax825442.IncomparableProperties
    14
    15open Lax153141.GraphParameters
    16
    17/-- Incomparability is symmetric and no parameter is incomparable with itself. -/
    18axiom incomparable_symmetric_irreflexive :
    19 (Symmetric Lax825442.Incomparable.Incomparable) ∧
    20 (Irreflexive Lax825442.Incomparable.Incomparable)
    21
    22end Lax825442.IncomparableProperties
    23
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