theorem extracted_formal_statement_0.{u_2} {ι : Type u_2} [inst : Nonempty ι] {g h : ι → ℝ} (hg : BddAbove (Set.range g))
  (hh : BddAbove (Set.range h)) : ⨆ i, g i + h i ≤ ⨆ i, ⨆ j, g i + h j := sorry

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

Tactic: apply ciSup_mono
    ·
  conv in fun i ↦ _ =>
    ext i
    rw [← add_ciSup hh]
  apply BddAbove.range_add hg
  simp
    ·
  intro i
  to_theorem rw [← add_ciSup hh]simp only [add_le_add_iff_left]exact le_ciSup hh i

State after:

Relevant lemmas:
error