theorem extracted_formal_statement_3 (x : ℝ) (hx : |x| ≤ 1) (hx_le_1 : x ≤ 1) :
  let f' := fun τ => rexp (τ * x) * x - (x + x ^ 2 * (rexp τ - 1));
  f' 0 = 0 := sorry

State before:
x τ : ℝ
hx : |x| ≤ 1
hτ : 0 ≤ τ
hx_le_1 : x ≤ 1
f : ℝ → ℝ := fun τ => rexp (τ * x) - (1 + τ * x + x ^ 2 * (rexp τ - 1 - τ))
f' : ℝ → ℝ := fun τ => rexp (τ * x) * x - (x + x ^ 2 * (rexp τ - 1))
f'' : ℝ → ℝ := fun τ => rexp (τ * x) * x * x - x ^ 2 * rexp τ
hf0 : f 0 = 0
⊢ f' 0 = 0

Tactic: simp [f']

State after:

Relevant lemmas: