-- Mathlib/MeasureTheory/Function/ConditionalExpectation/Unique.lean
theorem Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
    (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
    (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
    (hf_zero : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
    (hf_meas : AEStronglyMeasurable[m] f μ) : f =ᵐ[μ] 0

Proof state:
α : Type u_1
E' : Type u_2
𝕜 : Type u_4
p : ℝ≥0∞
m m0 : MeasurableSpace α
μ : Measure α
inst✝⁴ : RCLike 𝕜
inst✝³ : NormedAddCommGroup E'
inst✝² : InnerProductSpace 𝕜 E'
inst✝¹ : CompleteSpace E'
inst✝ : NormedSpace ℝ E'
hm : m ≤ m0
f : ↥(Lp E' p μ)
hp_ne_zero : p ≠ 0
hp_ne_top : p ≠ ⊤
hf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → IntegrableOn (↑↑f) s μ
hf_zero : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, ↑↑f x ∂μ = 0
hf_meas : AEStronglyMeasurable (↑↑f) μ
f_meas : ↥(lpMeas E' 𝕜 m p μ) := ⟨f, hf_meas⟩
hf_f_meas : ↑↑f =ᶠ[ae μ] ↑↑↑f_meas
⊢ ↑↑f =ᶠ[ae μ] 0

Tactic:
refine hf_f_meas.trans ?_

Result:
α : Type u_1
E' : Type u_2
𝕜 : Type u_4
p : ℝ≥0∞
m m0 : MeasurableSpace α
μ : Measure α
inst✝⁴ : RCLike 𝕜
inst✝³ : NormedAddCommGroup E'
inst✝² : InnerProductSpace 𝕜 E'
inst✝¹ : CompleteSpace E'
inst✝ : NormedSpace ℝ E'
hm : m ≤ m0
f : ↥(Lp E' p μ)
hp_ne_zero : p ≠ 0
hp_ne_top : p ≠ ⊤
hf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → IntegrableOn (↑↑f) s μ
hf_zero : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, ↑↑f x ∂μ = 0
hf_meas : AEStronglyMeasurable (↑↑f) μ
f_meas : ↥(lpMeas E' 𝕜 m p μ) := ⟨f, hf_meas⟩
hf_f_meas : ↑↑f =ᶠ[ae μ] ↑↑↑f_meas
⊢ ↑↑↑f_meas =ᶠ[ae μ] 0

Proof state:
α : Type u_1
E' : Type u_2
𝕜 : Type u_4
p : ℝ≥0∞
m m0 : MeasurableSpace α
μ : Measure α
inst✝⁴ : RCLike 𝕜
inst✝³ : NormedAddCommGroup E'
inst✝² : InnerProductSpace 𝕜 E'
inst✝¹ : CompleteSpace E'
inst✝ : NormedSpace ℝ E'
hm : m ≤ m0
f : ↥(Lp E' p μ)
hp_ne_zero : p ≠ 0
hp_ne_top : p ≠ ⊤
hf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → IntegrableOn (↑↑f) s μ
hf_zero : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, ↑↑f x ∂μ = 0
hf_meas : AEStronglyMeasurable (↑↑f) μ
f_meas : ↥(lpMeas E' 𝕜 m p μ) := ⟨f, hf_meas⟩
hf_f_meas : ↑↑f =ᶠ[ae μ] ↑↑↑f_meas
⊢ ↑↑↑f_meas =ᶠ[ae μ] 0

Tactic:
refine lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero hm f_meas hp_ne_zero hp_ne_top ?_ ?_

Result:
case refine_1
α : Type u_1
E' : Type u_2
𝕜 : Type u_4
p : ℝ≥0∞
m m0 : MeasurableSpace α
μ : Measure α
inst✝⁴ : RCLike 𝕜
inst✝³ : NormedAddCommGroup E'
inst✝² : InnerProductSpace 𝕜 E'
inst✝¹ : CompleteSpace E'
inst✝ : NormedSpace ℝ E'
hm : m ≤ m0
f : ↥(Lp E' p μ)
hp_ne_zero : p ≠ 0
hp_ne_top : p ≠ ⊤
hf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → IntegrableOn (↑↑f) s μ
hf_zero : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, ↑↑f x ∂μ = 0
hf_meas : AEStronglyMeasurable (↑↑f) μ
f_meas : ↥(lpMeas E' 𝕜 m p μ) := ⟨f, hf_meas⟩
hf_f_meas : ↑↑f =ᶠ[ae μ] ↑↑↑f_meas
⊢ ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → IntegrableOn (↑↑↑f_meas) s μ

case refine_2
α : Type u_1
E' : Type u_2
𝕜 : Type u_4
p : ℝ≥0∞
m m0 : MeasurableSpace α
μ : Measure α
inst✝⁴ : RCLike 𝕜
inst✝³ : NormedAddCommGroup E'
inst✝² : InnerProductSpace 𝕜 E'
inst✝¹ : CompleteSpace E'
inst✝ : NormedSpace ℝ E'
hm : m ≤ m0
f : ↥(Lp E' p μ)
hp_ne_zero : p ≠ 0
hp_ne_top : p ≠ ⊤
hf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → IntegrableOn (↑↑f) s μ
hf_zero : ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, ↑↑f x ∂μ = 0
hf_meas : AEStronglyMeasurable (↑↑f) μ
f_meas : ↥(lpMeas E' 𝕜 m p μ) := ⟨f, hf_meas⟩
hf_f_meas : ↑↑f =ᶠ[ae μ] ↑↑↑f_meas
⊢ ∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, ↑↑↑f_meas x ∂μ = 0