theorem extracted_formal_statement_14.{u_1} {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E]
  [inst_2 : CompleteSpace E] {f : E → ℝ} {f' : E → E} {x₀ : E} [p : Gradient_Descent_fix_stepsize f f' x₀] (k : ℕ) :
  (fun x => Gradient_Descent_fix_stepsize.a f f' x₀) k > 0 := sorry

State before:
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : InnerProductSpace ℝ E
inst✝ : CompleteSpace E
f : E → ℝ
f' : E → E
x₀ : E
p : Gradient_Descent_fix_stepsize f f' x₀
⊢ ∀ (k : ℕ), (fun x => Gradient_Descent_fix_stepsize.a f f' x₀) k > 0

Tactic: simp [p.step₁]

State after:

Relevant lemmas: