theorem extracted_formal_statement_57.{v} {ι : Type v} [inst : Nonempty ι] {f : ι → ℝ} {a : ℝ} (hf : ∀ (i : ι), |f i| ≤ a)
  (hbdd : BddAbove (Set.range f)) : -a ≤ ⨆ i, f i := sorry

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

Tactic: exact le_trans (abs_le.mp (hf i)).1 (le_ciSup hbdd i)

State after:

Relevant lemmas:
le_trans : ∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ c
le_ciSup : ∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {f : ι → α},
  BddAbove (Set.range f) → ∀ (c : ι), f c ≤ iSup f