theorem extracted_formal_statement_59.{v} {ι : Type v} [inst : Nonempty ι] {f : ι → ℝ} {a : ℝ} (hf : ∀ (i : ι), |f i| ≤ a)
  (hbdd : BddAbove (Set.range f)) (x : ι) : f x ≤ a := sorry

State before:
case right.H
ι : Type v
inst✝ : Nonempty ι
f : ι → ℝ
a : ℝ
hf : ∀ (i : ι), |f i| ≤ a
hbdd : BddAbove (Set.range f)
⊢ ∀ (x : ι), f x ≤ a

Tactic: exact fun x ↦ le_of_max_le_left (hf x)

State after:

Relevant lemmas:
le_of_max_le_left : ∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, a ⊔ b ≤ c → a ≤ c