theorem extracted_formal_statement_6.{u_1} {E : Type u_1} {f : E → ℝ} {g : ℕ → E}
  (mono : ∀ (k : ℕ), f (g (k + 1)) ≤ f (g k)) (n : ℕ)
  (h : (↑n + 1) * f (g (n.succ + 1)) / (↑n + 1 + 1) ≤ (∑ k ∈ Finset.range n.succ, f (g (k + 1))) / (↑n + 1 + 1)) :
  (↑n + 1) * f (g (n + 1 + 1)) / (↑n + 1 + 1) ≤ (∑ k ∈ Finset.range (n + 1), f (g (k + 1))) / (↑n + 1 + 1) := sorry

State before:
E : Type u_1
f : E → ℝ
g : ℕ → E
mono : ∀ (k : ℕ), f (g (k + 1)) ≤ f (g k)
n : ℕ
h : (↑n + 1) * f (g (n.succ + 1)) / (↑n + 1 + 1) ≤ (∑ k ∈ Finset.range n.succ, f (g (k + 1))) / (↑n + 1 + 1)
⊢ (↑n + 1) * f (g (n + 1 + 1)) / (↑n + 1 + 1) ≤ (∑ k ∈ Finset.range (n + 1), f (g (k + 1))) / (↑n + 1 + 1)

Tactic: exact h

State after:

Relevant lemmas: