theorem extracted_formal_statement_215.{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) (f_ge_zero : ∀ (n : β), 0 ≤ f n)
  (h_original_goal : ∀ (n : β), ⟨g n, hg n⟩ ≤ ⟨f n, f_ge_zero n⟩) (n : β) : g n ≤ f n := sorry

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
f_ge_zero : ∀ (n : β), 0 ≤ f n
⊢ ∀ (n : β), ⟨g n, ⋯⟩ ≤ ⟨f n, ⋯⟩

Tactic: simp only [Subtype.mk_le_mk]

State after:
[β : Type u_4
 f g : β → ℝ
 hg : ∀ (n : β), 0 ≤ g n
 hgf : ∀ (n : β), g n ≤ f n
 hf : Summable f
 f_ge_zero : ∀ (n : β), 0 ≤ f n
 ⊢ ∀ (n : β), g n ≤ f n]

Relevant lemmas:
Subtype.mk_le_mk : ∀ {α : Type u_2} [inst : LE α] {p : α → Prop} {x y : α} {hx : p x} {hy : p y},
  ⟨x, hx⟩ ≤ ⟨y, hy⟩ ↔ x ≤ y