theorem extracted_formal_statement_62.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] (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 → |X ω| ≤ c → |X ω| ≤ |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‖
e : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω
e' : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω ^ 2
ω : Ω
h : X ω ∈ Set.Icc a b
⊢ |X ω| ≤ c

Tactic: rw [←
  (by dsimp only [c]; to_theorem simp only [norm_eq_abs, abs_eq_self, le_max_iff, abs_nonneg, or_self] : |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‖
 e : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω
 e' : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω ^ 2
 ω : Ω
 h : X ω ∈ Set.Icc a b
 ⊢ |X ω| ≤ |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|
or_self : ∀ (p : Prop), (p ∨ p) = p
abs_eq_self : ∀ {G : Type u_1} [inst : LinearOrderedAddCommGroup G] {a : G}, |a| = a ↔ 0 ≤ a
Real.norm_eq_abs : ∀ (r : ℝ), ‖r‖ = |r|
le_max_iff : ∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, a ≤ b ⊔ c ↔ a ≤ b ∨ a ≤ c