theorem extracted_formal_statement_228.{w, v} {Z : Type w} {ι : Type v} {f : ι → Z → ℝ} [inst : Nonempty ι]
  {V : (Z → ℝ) → ℝ} (hV₀ : ∀ (f : Z → ℝ), V (-f) = -V f) (hV₁ : BddAbove (Set.range fun i => |V (f i)|))
  (hV₁' : BddAbove (Set.range fun i => V (if (↑i.1 == 0) = true then f i.2 else -f i.2))) (s : Fin 2) (i : ι)
  (h : ¬(↑s == 0) = true) : -V (f (s, i).2) ≤ |V (f i)| := sorry

State before:
Z : Type w
ι : Type v
f : ι → Z → ℝ
inst✝ : Nonempty ι
V : (Z → ℝ) → ℝ
hV₀ : ∀ (f : Z → ℝ), V (-f) = -V f
hV₁ : BddAbove (Set.range fun i => |V (f i)|)
hV₁' : BddAbove (Set.range fun i => V (if (↑i.1 == 0) = true then f i.2 else -f i.2))
s : Fin 2
i : ι
h : ¬(↑s == 0) = true
⊢ -V (f (s, i).2) ≤ |V (f i)|

Tactic: exact neg_le_abs (V (f i))

State after:

Relevant lemmas:
neg_le_abs : ∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] (a : α), -a ≤ |a|