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Functional equivalence is an equivalence relation

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

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    Natural Language Statement

    Theorem

    Functional equivalence of graph parameters is reflexive, symmetric, and transitive. Identity functions give reflexivity, symmetry exchanges the two bounds, and composition of nondecreasing bounding functions gives transitivity.

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

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    Lean source view on GitHub

    1import Lax825442.Equivalent
    2
    3/-!
    4---
    5title: Functional equivalence is an equivalence relation
    6type: theorem
    7---
    8Functional equivalence of graph parameters is reflexive, symmetric, and
    9transitive. Identity functions give reflexivity, symmetry exchanges the two
    10bounds, and composition of nondecreasing bounding functions gives transitivity.
    11-/
    12
    13namespace Lax825442.EquivalentEquivalence
    14
    15open Lax153141.GraphParameters
    16
    17/-- Mutual functional boundedness is an equivalence relation. -/
    18axiom equivalent_equivalence : Equivalence Lax825442.Equivalent.Equivalent
    19
    20end Lax825442.EquivalentEquivalence
    21
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