Lax Lean Archive

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

Lax56.MainTheorem

Large finite point sets have four collinear points or a visible six-clique

concepts/Lax56/MainTheorem.lean · lax-56

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

    Every finite set of at least 10(2450)10^(2^450) points in the real plane contains four distinct collinear points or six distinct points that pairwise see one another with respect to the whole set.

    Lean source view on GitHub

    1import Lax56.Geometry
    2
    3/-!
    4---
    5title: Large finite point sets have four collinear points or a visible six-clique
    6type: theorem
    7---
    8Every finite set of at least `10^(2^450)` points in the real plane contains
    9four distinct collinear points or six distinct points that pairwise see one
    10another with respect to the whole set.
    11-/
    12
    13namespace Lax56.MainTheorem
    14
    15open Lax56.Geometry
    16
    17axiom large_point_set_four_collinear_or_visible_six
    18 (P : Finset Point) (hP : 10 ^ (2 ^ 450) ≤ P.card) :
    19 HasFourCollinear P ∨ HasVisibleClique P 6
    20
    21end Lax56.MainTheorem
    22
    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…