-- File: FoML/FoML/Rademacher.lean
Theorem statement:
theorem extracted_formal_statement_32.{u_3, u_2} {α : Type u_2} [inst : MeasurableSpace α] (μ : Measure α)
  [inst_1 : IsFiniteMeasure μ] {ι : Sort u_3} [inst_2 : Countable ι] (f : ι → α → ℝ≥0∞)
  (hfm : ∀ (i : ι), Measurable (f i)) {b : ℝ≥0∞} (hb : b ≠ ⊤) (hf : ∀ (i : ι) (x : α), f i x ≤ b)
  (hf_le : ∀ (i : ι) (x : α), f i x < ⊤) (hfle : ∀ (i : ι), ∀ᵐ (x : α) ∂μ, f i x < ⊤)
  (hfne : ∀ᵐ (x : α) ∂μ, ∀ (i : ι), f i x ≠ ⊤) (hb' : b * μ Set.univ < ⊤)
  (h_original_goal : ⨆ i, ∫⁻ (a : α), f i a ∂μ ≠ ⊤) : ⨆ i, ∫⁻ (a : α), f i a ∂μ < ⊤ := sorry

Tactic state before:
α : Type u_2
inst✝² : MeasurableSpace α
μ : Measure α
inst✝¹ : IsFiniteMeasure μ
ι : Sort u_3
inst✝ : Countable ι
f : ι → α → ℝ≥0∞
hfm : ∀ (i : ι), Measurable (f i)
b : ℝ≥0∞
hb : b ≠ ⊤
hf : ∀ (i : ι) (x : α), f i x ≤ b
hf_le : ∀ (i : ι) (x : α), f i x < ⊤
hfle : ∀ (i : ι), ∀ᵐ (x : α) ∂μ, f i x < ⊤
hfne : ∀ᵐ (x : α) ∂μ, ∀ (i : ι), f i x ≠ ⊤
hb' : b * μ Set.univ < ⊤
⊢ ⨆ i, ∫⁻ (a : α), f i a ∂μ ≠ ⊤

Tactic: rw [← lt_top_iff_ne_top]

Tactic state after:
[α : Type u_2
 inst✝² : MeasurableSpace α
 μ : Measure α
 inst✝¹ : IsFiniteMeasure μ
 ι : Sort u_3
 inst✝ : Countable ι
 f : ι → α → ℝ≥0∞
 hfm : ∀ (i : ι), Measurable (f i)
 b : ℝ≥0∞
 hb : b ≠ ⊤
 hf : ∀ (i : ι) (x : α), f i x ≤ b
 hf_le : ∀ (i : ι) (x : α), f i x < ⊤
 hfle : ∀ (i : ι), ∀ᵐ (x : α) ∂μ, f i x < ⊤
 hfne : ∀ᵐ (x : α) ∂μ, ∀ (i : ι), f i x ≠ ⊤
 hb' : b * μ Set.univ < ⊤
 ⊢ ⨆ i, ∫⁻ (a : α), f i a ∂μ < ⊤]

Premises used:
lt_top_iff_ne_top : ∀ {α : Type u} [inst : PartialOrder α] [inst_3 : OrderTop α] {a : α}, a < ⊤ ↔ a ≠ ⊤