theorem extracted_formal_statement_58.{v} {ι : Type v} [inst : Nonempty ι] {f : ι → ℝ} {a : ℝ} (hf : ∀ (i : ι), |f i| ≤ a)
  (hbdd : BddAbove (Set.range f)) (h_original_goal : ⨆ i, f i ≤ a) (x : ι) : f x ≤ a := sorry

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

Tactic: apply ciSup_le

State after:
[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]

Relevant lemmas:
ciSup_le : ∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] [inst_1 : Nonempty ι] {f : ι → α}
  {c : α}, (∀ (x : ι), f x ≤ c) → iSup f ≤ c