-- File: FoML/FoML/Symmetrization.lean
Theorem statement:
theorem extracted_formal_statement_211.{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_original_goal : x ≤ a) : (fun i => V (if (↑i.1 == 0) = true then f i.2 else -f i.2)) (s, i) ≤ a := sorry

Tactic state before:
case h.intro.mk
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
⊢ x ≤ a

Tactic: rw [← eq]

Tactic state after:
[case h.intro.mk
 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
 ⊢ (fun i => V (if (↑i.1 == 0) = true then f i.2 else -f i.2)) (s, i) ≤ a]

Premises used: