Theorem: ProbabilityTheory.IsBernoulliSeq.nullMeasurableSet (LeanCamCombi/BernoulliSeq.lean)

State before:
α : Type u_1
Ω : Type u_2
inst✝ : MeasurableSpace Ω
X Y : Ω → Set α
μ : Measure Ω
p q : ℝ≥0
hX : IsBernoulliSeq X p μ
hY : IsBernoulliSeq Y q μ
a : α
⊢ NullMeasurableSet {ω | a ∈ X ω} μ
Tactic:
rw [(by ext; simp : {ω | a ∈ X ω} = (fun ω ↦ a ∈ X ω) ⁻¹' {True})]
State after:
α : Type u_1
Ω : Type u_2
inst✝ : MeasurableSpace Ω
X Y : Ω → Set α
μ : Measure Ω
p q : ℝ≥0
hX : IsBernoulliSeq X p μ
hY : IsBernoulliSeq Y q μ
a : α
⊢ NullMeasurableSet ((fun ω => a ∈ X ω) ⁻¹' {True}) μ

State before:
α : Type u_1
Ω : Type u_2
inst✝ : MeasurableSpace Ω
X Y : Ω → Set α
μ : Measure Ω
p q : ℝ≥0
hX : IsBernoulliSeq X p μ
hY : IsBernoulliSeq Y q μ
a : α
⊢ NullMeasurableSet ((fun ω => a ∈ X ω) ⁻¹' {True}) μ
Tactic:
exact (hX.aemeasurable a).nullMeasurableSet_preimage MeasurableSpace.measurableSet_top
State after:
no goals

State before:
α : Type u_1
Ω : Type u_2
inst✝ : MeasurableSpace Ω
X Y : Ω → Set α
μ : Measure Ω
p q : ℝ≥0
hX : IsBernoulliSeq X p μ
hY : IsBernoulliSeq Y q μ
a : α
⊢ {ω | a ∈ X ω} = (fun ω => a ∈ X ω) ⁻¹' {True}
Tactic:
ext
State after:
case h
α : Type u_1
Ω : Type u_2
inst✝ : MeasurableSpace Ω
X Y : Ω → Set α
μ : Measure Ω
p q : ℝ≥0
hX : IsBernoulliSeq X p μ
hY : IsBernoulliSeq Y q μ
a : α
x✝ : Ω
⊢ x✝ ∈ {ω | a ∈ X ω} ↔ x✝ ∈ (fun ω => a ∈ X ω) ⁻¹' {True}

State before:
case h
α : Type u_1
Ω : Type u_2
inst✝ : MeasurableSpace Ω
X Y : Ω → Set α
μ : Measure Ω
p q : ℝ≥0
hX : IsBernoulliSeq X p μ
hY : IsBernoulliSeq Y q μ
a : α
x✝ : Ω
⊢ x✝ ∈ {ω | a ∈ X ω} ↔ x✝ ∈ (fun ω => a ∈ X ω) ⁻¹' {True}
Tactic:
simp
State after:
no goals