theorem extracted_formal_statement_6.{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) : g i + ⨆ i, h i = ⨆ j, g i + h j := sorry

State before:
case h.e'_4.e_s.h
ι : Type u_2
inst✝ : Nonempty ι
g h : ι → ℝ
hg : BddAbove (Set.range g)
hh : BddAbove (Set.range h)
i : ι
⊢ g i + ⨆ i, h i = ⨆ j, g i + h j

Tactic: apply add_ciSup hh

State after:

Relevant lemmas:
add_ciSup : ∀ {ι : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : ConditionallyCompleteLattice G]
  [inst_2 : Nonempty ι] {f : ι → G} [inst_3 : AddLeftMono G],
  BddAbove (Set.range f) → ∀ (a : G), a + ⨆ i, f i = ⨆ i, a + f i