-- File: optlib/Optlib/Algorithm/Nesterov/NesterovAccelerationSecond.lean
Theorem statement:
theorem extracted_formal_statement_140.{u_1} {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E]
  [inst_2 : CompleteSpace E] {f h : E → ℝ} {f' : E → E} {x0 : E} {alg : Nesterov_second_fix_stepsize f h f' x0} {xm : E}
  (minφ : IsMinOn (f + h) univ xm) (k : ℕ)
  (h_original_goal :
    2 * 2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / ((↑k + 1 + 1) ^ 2 * 2) ≤
      2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / (↑k + 2) ^ 2) :
  2 * 2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / (↑k + 2) ^ 2 / 2 ≤
    2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / (↑k + 2) ^ 2 := sorry

Tactic state before:
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : InnerProductSpace ℝ E
inst✝ : CompleteSpace E
f h : E → ℝ
f' : E → E
x0 : E
alg : Nesterov_second_fix_stepsize f h f' x0
xm : E
minφ : IsMinOn (f + h) univ xm
k : ℕ
⊢ 2 * 2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / ((↑k + 1 + 1) ^ 2 * 2) ≤
    2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / (↑k + 2) ^ 2

Tactic: rw [add_assoc, one_add_one_eq_two, ← div_div]

Tactic state after:
[E : Type u_1
 inst✝² : NormedAddCommGroup E
 inst✝¹ : InnerProductSpace ℝ E
 inst✝ : CompleteSpace E
 f h : E → ℝ
 f' : E → E
 x0 : E
 alg : Nesterov_second_fix_stepsize f h f' x0
 xm : E
 minφ : IsMinOn (f + h) univ xm
 k : ℕ
 ⊢ 2 * 2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / (↑k + 2) ^ 2 / 2 ≤
     2 * ↑(Nesterov_second_fix_stepsize.l f h f' x0) / (↑k + 2) ^ 2]

Premises used:
div_div : ∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b c : α), a / b / c = a / (b * c)
add_assoc : ∀ {G : Type u_1} [inst : AddSemigroup G] (a b c : G), a + b + c = a + (b + c)
one_add_one_eq_two : ∀ {R : Type u_1} [inst : AddMonoidWithOne R], 1 + 1 = 2