theorem extracted_formal_statement_0.{u_1} {E : Type u_1} {f : E → ℝ} {g : ℕ → E}
  (mono : ∀ (k : ℕ), f (g (k + 1)) ≤ f (g k))
  (h_original_goal : ∑ k ∈ Finset.range (0 + 1), f (g (k + 1)) ≥ (↑0 + 1) * f (g (0 + 2))) : f (g 2) ≤ f (g 1) := sorry

State before:
case zero
E : Type u_1
f : E → ℝ
g : ℕ → E
mono : ∀ (k : ℕ), f (g (k + 1)) ≤ f (g k)
⊢ ∑ k ∈ Finset.range (0 + 1), f (g (k + 1)) ≥ (↑0 + 1) * f (g (0 + 2))

Tactic: simp

State after:
[case zero
 E : Type u_1
 f : E → ℝ
 g : ℕ → E
 mono : ∀ (k : ℕ), f (g (k + 1)) ≤ f (g k)
 ⊢ f (g 2) ≤ f (g 1)]

Relevant lemmas: