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Lax68.Ladders

Ladders

concepts/Lax68/Ladders.lean · lax-68

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    Definition

    A finite ladder is a nonempty two-row grid: two paths joined by corresponding rungs.

    Lean source view on GitHub

    1import Mathlib.Combinatorics.SimpleGraph.Hasse
    2
    3/-!
    4---
    5title: Ladders
    6type: definition
    7---
    8A finite ladder is a nonempty two-row grid: two paths joined by corresponding
    9rungs.
    10-/
    11
    12set_option autoImplicit false
    13
    14namespace Lax68.Ladders
    15
    16def HasLadderShape {V : Type*} (G : SimpleGraph V) : Prop :=
    17 ∃ n : ℕ,
    18 0 < n ∧
    19 Nonempty
    20 (G ≃g (SimpleGraph.pathGraph n □ SimpleGraph.pathGraph 2))
    21
    22def IsLadder {V : Type*} (G : SimpleGraph V) : Prop :=
    23 HasLadderShape G
    24
    25end Lax68.Ladders
    26

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