theorem extracted_formal_statement_94.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] (t a b : ℝ) {X : Ω → ℝ} (hX : AEMeasurable X μ) (h_1 : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b) :
  let c := ‖a‖ ⊔ ‖b‖;
  ∀ (ω : Ω), X ω ∈ Set.Icc a b → t * X ω ≤ |t| * c → t * X ω ≤ |t| * |c| := sorry

State before:
case h
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
t a b : ℝ
X : Ω → ℝ
hX : AEMeasurable X μ
h✝ : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
c : ℝ := ‖a‖ ⊔ ‖b‖
ω : Ω
h : X ω ∈ Set.Icc a b
⊢ t * X ω ≤ |t| * c

Tactic: rw [← (abs_eq_self.mpr (le_trans' (le_max_left |a| ‖b‖) (abs_nonneg a)) : |c| = c)]

State after:
[case h
 Ω : Type u_1
 m : MeasurableSpace Ω
 μ : Measure Ω
 inst✝ : IsFiniteMeasure μ
 t a b : ℝ
 X : Ω → ℝ
 hX : AEMeasurable X μ
 h✝ : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
 c : ℝ := ‖a‖ ⊔ ‖b‖
 ω : Ω
 h : X ω ∈ Set.Icc a b
 ⊢ t * X ω ≤ |t| * |c|]

Relevant lemmas:
abs_nonneg : ∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [inst_2 : AddLeftMono α]
  [inst_3 : AddRightMono α] (a : α), 0 ≤ |a|
le_trans' : ∀ {α : Type u_2} [inst : Preorder α] {a b c : α}, b ≤ c → a ≤ b → a ≤ c
le_max_left : ∀ {α : Type u_1} [inst : LinearOrder α] (a b : α), a ≤ a ⊔ b