theorem extracted_formal_statement_286.{u_1, w, u} {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {n : ℕ}
  {ι : Type u_1} {f : ι → Z → ℝ} {μ : Measure Ω} [inst_1 : IsProbabilityMeasure μ] [inst_2 : Nonempty ι]
  [inst_3 : Countable ι] {X : Ω → Z} (hf : ∀ (i : ι), Measurable (f i ∘ X)) {b : ℝ}
  (hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b) (σ : Signs n) (a : σ ∈ Finset.univ) :
  BddAbove (Set.range fun i => ∑ k, b) := sorry

State before:
case h.B
Ω : Type u
inst✝³ : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
inst✝¹ : Nonempty ι
inst✝ : Countable ι
X : Ω → Z
hf : ∀ (i : ι), Measurable (f i ∘ X)
b : ℝ
hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b
ω : (Fin n → Ω) × (Fin n → Ω)
σ : Signs n
a✝ : σ ∈ Finset.univ
⊢ BddAbove (Set.range fun i => ∑ k, b)

Tactic: simp only [Finset.sum_const, Finset.card_univ, Fintype.card_fin, nsmul_eq_mul, Set.range_const,
  bddAbove_singleton]

State after:

Relevant lemmas:
Finset.card_univ : ∀ {α : Type u_1} [inst : Fintype α], Finset.univ.card = Fintype.card α
Fintype.card_fin : ∀ (n : ℕ), Fintype.card (Fin n) = n
nsmul_eq_mul : ∀ {α : Type u_1} [inst : NonAssocSemiring α] (n : ℕ) (a : α), n • a = ↑n * a
bddAbove_singleton : ∀ {α : Type u} [inst : Preorder α] {a : α}, BddAbove {a}
Set.range_const : ∀ {α : Type u_1} {ι : Sort u_4} [inst : Nonempty ι] {c : α}, (Set.range fun x => c) = {c}
Finset.sum_const : ∀ {α : Type u_3} {β : Type u_4} {s : Finset α} [inst : AddCommMonoid β] (b : β),
  ∑ _x ∈ s, b = s.card • b