case intro.intro.intro
G : Type w
inst✝¹ : TopologicalSpace G
μ : Content G
inst✝ : T2Space G
A : Set G
hA : ↑(Content.outerMeasure μ) A ≠ ⊤
ε : ℝ≥0
hε : ε ≠ 0
U : Set G
hU : IsOpen U
h2U : A ⊆ U
h3U :
  ↑(inducedOuterMeasure (fun s₁ hs₁ => innerContent μ { carrier := s₁, is_open' := hs₁ }) (_ : IsOpen ∅)
          (_ : innerContent μ ⊥ = 0))
      U ≤
    ↑(inducedOuterMeasure (fun s₁ hs₁ => innerContent μ { carrier := s₁, is_open' := hs₁ }) (_ : IsOpen ∅)
            (_ : innerContent μ ⊥ = 0))
        A +
      ↑ε
⊢ ∃ U, A ⊆ ↑U ∧ ↑(Content.outerMeasure μ) ↑U ≤ ↑(Content.outerMeasure μ) A + ↑ε
G : Type w
inst✝¹ : TopologicalSpace G
μ : Content G
inst✝ : T2Space G
A : Set G
hA : ↑(Content.outerMeasure μ) A ≠ ⊤
ε : ℝ≥0
hε : ε ≠ 0
⊢ ∃ U, A ⊆ ↑U ∧ ↑(Content.outerMeasure μ) ↑U ≤ ↑(Content.outerMeasure μ) A + ↑ε
rcases inducedOuterMeasure_exists_set _ μ.innerContent_iUnion_nat μ.innerContent_mono hA
    (ENNReal.coe_ne_zero.2 hε) with
  ⟨U, hU, h2U, h3U⟩
no goals
case intro.intro.intro
G : Type w
inst✝¹ : TopologicalSpace G
μ : Content G
inst✝ : T2Space G
A : Set G
hA : ↑(Content.outerMeasure μ) A ≠ ⊤
ε : ℝ≥0
hε : ε ≠ 0
U : Set G
hU : IsOpen U
h2U : A ⊆ U
h3U :
  ↑(inducedOuterMeasure (fun s₁ hs₁ => innerContent μ { carrier := s₁, is_open' := hs₁ }) (_ : IsOpen ∅)
          (_ : innerContent μ ⊥ = 0))
      U ≤
    ↑(inducedOuterMeasure (fun s₁ hs₁ => innerContent μ { carrier := s₁, is_open' := hs₁ }) (_ : IsOpen ∅)
            (_ : innerContent μ ⊥ = 0))
        A +
      ↑ε
⊢ ∃ U, A ⊆ ↑U ∧ ↑(Content.outerMeasure μ) ↑U ≤ ↑(Content.outerMeasure μ) A + ↑ε
exact ⟨⟨U, hU⟩, h2U, h3U⟩