-- File: optlib/Optlib/Algorithm/Nesterov/NesterovAccelerationFirst.lean
Theorem statement:
theorem extracted_formal_statement_155.{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_first_fix_stepsize f h f' x0} {xm : E}
  (minφ : IsMinOn (f + h) univ xm) : 0 ≤ ‖x0 - xm‖ ^ 2 := sorry

Tactic state before:
case a0
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_first_fix_stepsize f h f' x0
xm : E
minφ : IsMinOn (f + h) univ xm
k : ℕ
⊢ 0 ≤ ‖x0 - xm‖ ^ 2

Tactic: apply sq_nonneg

Tactic state after:

Premises used:
sq_nonneg : ∀ {α : Type u} [inst : Semiring α] [inst_3 : LinearOrder α] [inst_4 : IsRightCancelAdd α]
  [inst_5 : ZeroLEOneClass α] [inst_6 : ExistsAddOfLE α] [inst_7 : PosMulMono α] [inst_8 : AddLeftStrictMono α] (a : α),
  0 ≤ a ^ 2