theorem extracted_formal_statement_7.{u_1} {E : Type u_1} {xm : E} {f : E → ℝ} {g : ℕ → E}
  (mono : ∀ (k : ℕ), f (g (k + 1)) ≤ f (g k)) :
  f (g (0 + 1)) - f xm ≤ (∑ k ∈ Finset.range (0 + 1), (f (g (k + 1)) - f xm)) / (↑0 + 1) := sorry

State before:
case zero
E : Type u_1
xm : E
f : E → ℝ
g : ℕ → E
mono : ∀ (k : ℕ), f (g (k + 1)) ≤ f (g k)
⊢ f (g (0 + 1)) - f xm ≤ (∑ k ∈ Finset.range (0 + 1), (f (g (k + 1)) - f xm)) / (↑0 + 1)

Tactic: simp

State after:

Relevant lemmas: