fst_notMem_right — Mathlib

English

Any graph containing an IsFiveWheelLike structure is not (r+1)-colorable.

Русский

Любой граф, содержащий структуру IsFiveWheelLike, не цветоспособен в (r+1) цветов.

LaTeX

$$$$ \\forall G(IsFiveWheelLike r k v w_1 w_2 s t)\\; :\\; G.Colorable (r+1) = \\text{false}. $$$$

Lean4

@[grind]
theorem fst_notMem_right : w₁ ∉ t := fun h ↦
  hw.isPathGraph3Compl.not_adj_fst <|
    hw.isNClique_right.1 (mem_insert_self ..) (mem_insert_of_mem h) hw.isPathGraph3Compl.ne_fst

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