innerContent_bot — Mathlib

English

For open sets U ⊆ V, μ.innerContent(U) ≤ μ.innerContent(V).

Русский

Для открытых U ⊆ V выполнено μ.innerContent(U) ≤ μ.innerContent(V).

LaTeX

$$$U \subseteq V \;\Rightarrow\; μ.innerContent(U) \le μ.innerContent(V)$$$

Lean4

theorem innerContent_bot : μ.innerContent ⊥ = 0 :=
  by
  refine le_antisymm ?_ (zero_le _)
  rw [← μ.empty]
  refine iSup₂_le fun K hK => ?_
  have : K = ⊥ := by
    ext1
    rw [subset_empty_iff.mp hK, Compacts.coe_bot]
  rw [this]

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