theorem extracted_formal_statement_6.{u_1} {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ : Measure Ω)
  [inst_1 : IsProbabilityMeasure μ] {n : ℕ} {X : Fin n → Ω → ℝ} (hXm : ∀ (i : Fin n), Measurable (X i))
  (hX_bdd : ∀ (i : Fin n), ∀ᵐ (ω : Ω) ∂μ, |X i ω| ≤ 1) (τ : ℝ) (hlam : τ ≥ 0) (i : Fin n) (ω : Ω) (hω : |X i ω| ≤ 1)
  (this : -1 ≤ X i ω ∧ X i ω ≤ 1) : -τ ≤ τ * X i ω := sorry

State before:
case h.left
Ω : Type u_1
inst : MeasurableSpace Ω
μ : Measure Ω
inst_1 : IsProbabilityMeasure μ
n : ℕ
X : Fin n → Ω → ℝ
hXm : ∀ (i : Fin n), Measurable (X i)
hX_bdd : ∀ (i : Fin n), ∀ᵐ (ω : Ω) ∂μ, |X i ω| ≤ 1
τ : ℝ
hlam : τ ≥ 0
i : Fin n
ω : Ω
hω : |X i ω| ≤ 1
this : -1 ≤ X i ω ∧ X i ω ≤ 1
⊢ -τ ≤ τ * X i ω

Tactic: rw [mul_comm]
    have h := mul_le_mul_of_nonneg_left this.1 (hlam)
    linarith [h]

State after:

Relevant lemmas:
mul_le_mul_of_nonneg_left : ∀ {α : Type u_3} {a b c : α} [inst : Mul α] [inst_2 : Zero α] [inst_3 : Preorder α]
  [inst_4 : PosMulMono α], b ≤ c → 0 ≤ a → a * b ≤ a * c
mul_comm : ∀ {G : Type u_1} [inst : CommMagma G] (a b : G), a * b = b * a