-- File: FoML/FoML/Symmetrization.lean
Theorem statement:
theorem extracted_formal_statement_213.{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) (a : ℝ)
  (ha : ∀ ⦃a_1 : ℝ⦄, (a_1 ∈ Set.range fun i => |V (f i)|) → a_1 ≤ a) ⦃x : ℝ⦄ (s : Fin 2) (i : ι)
  (eq : (fun i => V (if (↑i.1 == 0) = true then f i.2 else -f i.2)) (s, i) = x) (hax : |V (f i)| ≤ a)
  (h : (↑s == 0) = true) : V (f i) ≤ a := sorry

Tactic 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
a : ℝ
ha : ∀ ⦃a_1 : ℝ⦄, (a_1 ∈ Set.range fun i => |V (f i)|) → a_1 ≤ a
x : ℝ
s : Fin 2
i : ι
eq : (fun i => V (if (↑i.1 == 0) = true then f i.2 else -f i.2)) (s, i) = x
hax : |V (f i)| ≤ a
h : (↑s == 0) = true
⊢ V (f i) ≤ a

Tactic: exact le_of_max_le_left hax

Tactic state after:

Premises used:
le_of_max_le_left : ∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, a ⊔ b ≤ c → a ≤ c