Theorem: MeasureTheory.Measure.measure_toMeasurable_add_inter_left
File: Mathlib/MeasureTheory/Measure/MeasureSpace.lean

tactic: refine (measure_inter_eq_of_measure_eq hs ?_ (subset_toMeasurable _ _) ?_).symm
state_before: α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : (μ + ν) t ≠ ⊤
⊢ μ (toMeasurable (μ + ν) t ∩ s) = μ (t ∩ s)
state_after: case refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : (μ + ν) t ≠ ⊤
⊢ μ t = μ (toMeasurable (μ + ν) t)

case refine_2
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : (μ + ν) t ≠ ⊤
⊢ μ t ≠ ⊤

tactic: refine
  measure_eq_left_of_subset_of_measure_add_eq ?_ (subset_toMeasurable _ _)
    (measure_toMeasurable t).symm
state_before: case refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : (μ + ν) t ≠ ⊤
⊢ μ t = μ (toMeasurable (μ + ν) t)
state_after: case refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : (μ + ν) t ≠ ⊤
⊢ (μ + ν) (toMeasurable (μ + ν) t) ≠ ⊤

tactic: rwa [measure_toMeasurable t]
state_before: case refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : (μ + ν) t ≠ ⊤
⊢ (μ + ν) (toMeasurable (μ + ν) t) ≠ ⊤
state_after: no goals

tactic: simp only [not_or, ENNReal.add_eq_top, Pi.add_apply, Ne, coe_add] at ht
state_before: case refine_2
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : (μ + ν) t ≠ ⊤
⊢ μ t ≠ ⊤
state_after: case refine_2
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : ¬μ t = ⊤ ∧ ¬ν t = ⊤
⊢ μ t ≠ ⊤

tactic: exact ht.1
state_before: case refine_2
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Type u_5
R : Type u_6
R' : Type u_7
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t✝ s t : Set α
hs : MeasurableSet s
ht : ¬μ t = ⊤ ∧ ¬ν t = ⊤
⊢ μ t ≠ ⊤
state_after: no goals