nonUniforms_bot — Mathlib

English

For the bottom partition, the IsUniform predicate has a specific card-bound form with the bot and empty partition.

Русский

Для нижнего разбиения IsUniform имеет форму, ограниченную по карте с бот-разбиением и пустым разбиением.

LaTeX

$$Finpartition.IsUniform (P := Finpartition.instBotFinset A) G ε$$

Lean4

theorem nonUniforms_bot (hε : 0 < ε) : (⊥ : Finpartition A).nonUniforms G ε = ∅ :=
  by
  rw [eq_empty_iff_forall_notMem]
  rintro ⟨u, v⟩
  simp only [mk_mem_nonUniforms, parts_bot, mem_map, not_and, Classical.not_not, exists_imp]; dsimp
  rintro x ⟨_, rfl⟩ y ⟨_, rfl⟩ _
  rwa [SimpleGraph.isUniform_singleton]

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