Lax Lean Archive

Paths are trees

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

proven

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    Natural Language Statement

    Theorem

    Every path graph is a tree.

    Concept map
    3 concepts
    100%
    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 Lax68.Paths
    2import Lax68.Trees
    3
    4/-!
    5---
    6title: Paths are trees
    7type: theorem
    8---
    9Every path graph is a tree.
    10-/
    11
    12set_option autoImplicit false
    13
    14namespace Lax68.PathTree
    15
    16/-- Every path graph is a tree. -/
    17axiom path_tree {V : Type*} {G : SimpleGraph V} :
    18 Lax68.Paths.IsPath G →
    19 Lax68.Trees.IsTree G
    20
    21end Lax68.PathTree
    22
    Show Proof
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