Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Lax17.StrongPathOfSetsContainsGrid

A grid minor from a strong path-of-sets system

concepts/Lax17/StrongPathOfSetsContainsGrid.lean · lax-17

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    Each proof establishes this claim relative to its assumptions.

    Theorem

    A sufficiently long and wide strong path-of-sets system contains a prescribed square grid minor.

    Lean source view on GitHub

    1import Lax17.GridMinor
    2import Lax17.PathOfSets
    3
    4/-!
    5---
    6title: A grid minor from a strong path-of-sets system
    7type: theorem
    8---
    9A sufficiently long and wide strong path-of-sets system contains a
    10prescribed square grid minor.
    11-/
    12
    13namespace Lax17.StrongPathOfSetsContainsGrid
    14
    15universe u
    16
    17/-- A strong path-of-sets system of length at least `2g(g-1)` and width at
    18least `16g² + 10g` contains the `g × g` grid as a minor. -/
    19axiom strongPathOfSetsContainsGrid :
    20 ∀ {V : Type u} [Fintype V] [DecidableEq V]
    21 (G : SimpleGraph V) {ℓ w g : ℕ},
    22 Nonempty (Lax17.PathOfSets.StrongSystem G ℓ w) →
    23 2 ≤ g →
    24 2 * g * (g - 1) ≤ ℓ →
    25 16 * g ^ 2 + 10 * g ≤ w →
    26 Lax17.GridMinor.ContainsGridMinor G g
    27
    28end Lax17.StrongPathOfSetsContainsGrid
    29
    Show Proof

    Builds on

    Used by

    none

    From Mathlib

    none

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…