theorem extracted_formal_statement_4.{u_2} {ι : Type u_2} [inst : Nonempty ι] {g h : ι → ℝ} (hg : BddAbove (Set.range g))
  (hh : BddAbove (Set.range h)) (i : ι) : h i ≤ ⨆ i, h i := sorry

State before:
case H
ι : Type u_2
inst✝ : Nonempty ι
g h : ι → ℝ
hg : BddAbove (Set.range g)
hh : BddAbove (Set.range h)
i : ι
⊢ h i ≤ ⨆ i, h i

Tactic: exact le_ciSup hh i

State after:

Relevant lemmas:
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