theorem extracted_formal_statement_8.{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)
  (hf : ∀ (i : ι), Measurable fun a => f i a) {b : ℝ} (hf' : ∀ (i : ι) (x : α), |f i x| ≤ b) :
  ⨆ i, ∫ (ω : α), (ENNReal.ofReal |f i ω|).toReal ∂μ ≤ ∫ (ω : α), ⨆ i, (ENNReal.ofReal |f i ω|).toReal ∂μ := sorry

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
hf : ∀ (i : ι), Measurable fun a => f i a
b : ℝ
hf' : ∀ (i : ι) (x : α), |f i x| ≤ b
⊢ ⨆ i, ∫ (ω : α), (ENNReal.ofReal |f i ω|).toReal ∂μ ≤ ∫ (ω : α), ⨆ i, (ENNReal.ofReal |f i ω|).toReal ∂μ

Tactic: apply
  iSup_integral_le_aux μ (fun i a ↦ .ofReal |f i a|) (fun i ↦ (hf i).norm.ennreal_ofReal)
    (ENNReal.ofReal_ne_top : .ofReal (b + 1) ≠ ⊤) (fun i x ↦ ENNReal.ofReal_le_ofReal (le_of_lt ?_))
    have hf' := hf' i x
    linarith

State after:

Relevant lemmas:
error