-- File: optlib/Optlib/Algorithm/ADMM/Theroem_converge.lean
Theorem statement:
theorem extracted_formal_statement_214.{u_4} {β : Type u_4} {f g : β → ℝ} (hg : ∀ (n : β), 0 ≤ g n)
  (hgf : ∀ (n : β), g n ≤ f n) (hf : Summable f) (n : β) : 0 ≤ f n := sorry

Tactic state before:
β : Type u_4
f g : β → ℝ
hg : ∀ (n : β), 0 ≤ g n
hgf : ∀ (n : β), g n ≤ f n
hf : Summable f
n : β
⊢ 0 ≤ f n

Tactic: apply le_trans (hg n) (hgf n)

Tactic state after:

Premises used:
le_trans : ∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ c