theorem extracted_formal_statement_143.{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} [p : Nesterov_first_fix_stepsize f h f' x0] (k : ℕ)
  (h_original_goal :
    0 < Nesterov_first_fix_stepsize.t f h f' x0 k ∧
      Nesterov_first_fix_stepsize.t f h f' x0 k ≤ 1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0)) :
  0 < 1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0) ∧
    1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0) ≤ 1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0) := sorry

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
f h : E → ℝ
f' : E → E
x0 : E
p : Nesterov_first_fix_stepsize f h f' x0
k : ℕ
⊢ 0 < Nesterov_first_fix_stepsize.t f h f' x0 k ∧
    Nesterov_first_fix_stepsize.t f h f' x0 k ≤ 1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0)

Tactic: rw [p.teq k]

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
 f h : E → ℝ
 f' : E → E
 x0 : E
 p : Nesterov_first_fix_stepsize f h f' x0
 k : ℕ
 ⊢ 0 < 1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0) ∧
     1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0) ≤ 1 / ↑(Nesterov_first_fix_stepsize.l f h f' x0)]

Relevant lemmas: