ι : Sort u_3
α : Type u_1
β : Type u_2
γ : Type ?u.154841
inst✝¹ : MeasurableSpace α
inst✝ : MeasurableSpace β
f : ι → α → β
μ : MeasureTheory.Measure α
p : α → (ι → β) → Prop
hf : ∀ (i : ι), AEMeasurable (f i)
x : α
hx : x ∈ aeSeqSet hf p
i : ι
⊢ {x | ∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x}ᶜ ⊆
    toMeasurable μ ({x | (∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x) ∧ p x fun n => f n x}ᶜ)
ι : Sort u_3
α : Type u_1
β : Type u_2
γ : Type ?u.154841
inst✝¹ : MeasurableSpace α
inst✝ : MeasurableSpace β
f : ι → α → β
μ : MeasureTheory.Measure α
p : α → (ι → β) → Prop
hf : ∀ (i : ι), AEMeasurable (f i)
x : α
hx : x ∈ aeSeqSet hf p
i : ι
⊢ aeSeqSet hf p ⊆ {x | ∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x}
rw [aeSeqSet, ← compl_compl { x | ∀ i, f i x = (hf i).mk (f i) x }, Set.compl_subset_compl]
ι : Sort u_3
α : Type u_1
β : Type u_2
γ : Type ?u.154841
inst✝¹ : MeasurableSpace α
inst✝ : MeasurableSpace β
f : ι → α → β
μ : MeasureTheory.Measure α
p : α → (ι → β) → Prop
hf : ∀ (i : ι), AEMeasurable (f i)
x✝ : α
hx : x✝ ∈ aeSeqSet hf p
i : ι
x : α
h : x ∈ {x | (∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x) ∧ p x fun n => f n x}
⊢ x ∈ {x | ∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x}
ι : Sort u_3
α : Type u_1
β : Type u_2
γ : Type ?u.154841
inst✝¹ : MeasurableSpace α
inst✝ : MeasurableSpace β
f : ι → α → β
μ : MeasureTheory.Measure α
p : α → (ι → β) → Prop
hf : ∀ (i : ι), AEMeasurable (f i)
x : α
hx : x ∈ aeSeqSet hf p
i : ι
⊢ {x | ∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x}ᶜ ⊆
    toMeasurable μ ({x | (∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x) ∧ p x fun n => f n x}ᶜ)
refine' Set.Subset.trans (Set.compl_subset_compl.mpr fun x h => _) (subset_toMeasurable _ _)
no goals
ι : Sort u_3
α : Type u_1
β : Type u_2
γ : Type ?u.154841
inst✝¹ : MeasurableSpace α
inst✝ : MeasurableSpace β
f : ι → α → β
μ : MeasureTheory.Measure α
p : α → (ι → β) → Prop
hf : ∀ (i : ι), AEMeasurable (f i)
x✝ : α
hx : x✝ ∈ aeSeqSet hf p
i : ι
x : α
h : x ∈ {x | (∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x) ∧ p x fun n => f n x}
⊢ x ∈ {x | ∀ (i : ι), f i x = AEMeasurable.mk (f i) (_ : AEMeasurable (f i)) x}
exact h.1