Theorem: MeasureTheory.Measure.Subtype.volume_univ
File: Mathlib/MeasureTheory/Measure/Restrict.lean

tactic: rw [Subtype.volume_def, comap_apply₀ _ _ _ _ MeasurableSet.univ.nullMeasurableSet]
state_before: R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ volume univ = volume u
state_after: R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ volume (Subtype.val '' univ) = volume u

R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ Injective Subtype.val

R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ ∀ (s : Set { x // x ∈ u }), MeasurableSet s → NullMeasurableSet (Subtype.val '' s) volume

tactic: congr
state_before: R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ volume (Subtype.val '' univ) = volume u
state_after: case h.e_6.h
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ Subtype.val '' univ = u

tactic: simp only [image_univ, Subtype.range_coe_subtype, setOf_mem_eq]
state_before: case h.e_6.h
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ Subtype.val '' univ = u
state_after: no goals

tactic: exact Subtype.coe_injective
state_before: R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ Injective Subtype.val
state_after: no goals

tactic: exact fun t => MeasurableSet.nullMeasurableSet_subtype_coe hu
state_before: R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
u : Set δ
inst✝ : MeasureSpace δ
p : δ → Prop
hu : NullMeasurableSet u volume
⊢ ∀ (s : Set { x // x ∈ u }), MeasurableSet s → NullMeasurableSet (Subtype.val '' s) volume
state_after: no goals