-- File: FoML/FoML/Hoeffding.lean
Theorem statement:
theorem extracted_formal_statement_10 (a b : ℝ) (m : ℕ) (hm : m > 0) (hab : b > a)
  (h_original_goal : 0 < (b - a) ^ 2 * ↑m) : 0 < ↑m := sorry

Tactic state before:
case hb
ε a b : ℝ
m : ℕ
hm : m > 0
hε : ε > 0
hab : b > a
g : { t // t > 0 } → ℝ := fun t => -↑t * ε + ↑t ^ 2 * ↑m * (b - a) ^ 2 / 8
⊢ 0 < (b - a) ^ 2 * ↑m

Tactic: apply mul_pos

Tactic state after:
[case hb.ha
 ε a b : ℝ
 m : ℕ
 hm : m > 0
 hε : ε > 0
 hab : b > a
 g : { t // t > 0 } → ℝ := fun t => -↑t * ε + ↑t ^ 2 * ↑m * (b - a) ^ 2 / 8
 ⊢ 0 < (b - a) ^ 2,
 case hb.hb
 ε a b : ℝ
 m : ℕ
 hm : m > 0
 hε : ε > 0
 hab : b > a
 g : { t // t > 0 } → ℝ := fun t => -↑t * ε + ↑t ^ 2 * ↑m * (b - a) ^ 2 / 8
 ⊢ 0 < ↑m]

Premises used:
mul_pos : ∀ {α : Type u_3} {a b : α} [inst : MulZeroClass α] [inst_1 : Preorder α] [inst_2 : PosMulStrictMono α],
  0 < a → 0 < b → 0 < a * b