Theorem: MeasureTheory.Measure.ext_of_Ico_finite
File: Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean

tactic: refine'
  ext_of_generate_finite _ (BorelSpace.measurable_eq.trans (borel_eq_generateFrom_Ico α))
    (isPiSystem_Ico (id : α → α) id) _ hμν
state_before: α✝ : Type ?u.676748
β : Type ?u.676751
γ : Type ?u.676754
γ₂ : Type ?u.676757
δ : Type ?u.676760
ι : Sort y
s t u : Set α✝
inst✝²² : TopologicalSpace α✝
inst✝²¹ : MeasurableSpace α✝
inst✝²⁰ : OpensMeasurableSpace α✝
inst✝¹⁹ : TopologicalSpace β
inst✝¹⁸ : MeasurableSpace β
inst✝¹⁷ : OpensMeasurableSpace β
inst✝¹⁶ : TopologicalSpace γ
inst✝¹⁵ : MeasurableSpace γ
inst✝¹⁴ : BorelSpace γ
inst✝¹³ : TopologicalSpace γ₂
inst✝¹² : MeasurableSpace γ₂
inst✝¹¹ : BorelSpace γ₂
inst✝¹⁰ : MeasurableSpace δ
α' : Type ?u.676853
inst✝⁹ : TopologicalSpace α'
inst✝⁸ : MeasurableSpace α'
inst✝⁷ : LinearOrder α✝
inst✝⁶ : OrderClosedTopology α✝
a b x : α✝
α : Type u_1
inst✝⁵ : TopologicalSpace α
m : MeasurableSpace α
inst✝⁴ : SecondCountableTopology α
inst✝³ : LinearOrder α
inst✝² : OrderTopology α
inst✝¹ : BorelSpace α
μ ν : Measure α
inst✝ : IsFiniteMeasure μ
hμν : ↑↑μ univ = ↑↑ν univ
h : ∀ ⦃a b : α⦄, a < b → ↑↑μ (Ico a b) = ↑↑ν (Ico a b)
⊢ μ = ν

tactic: rintro - ⟨a, b, hlt, rfl⟩
state_before: α✝ : Type ?u.676748
β : Type ?u.676751
γ : Type ?u.676754
γ₂ : Type ?u.676757
δ : Type ?u.676760
ι : Sort y
s t u : Set α✝
inst✝²² : TopologicalSpace α✝
inst✝²¹ : MeasurableSpace α✝
inst✝²⁰ : OpensMeasurableSpace α✝
inst✝¹⁹ : TopologicalSpace β
inst✝¹⁸ : MeasurableSpace β
inst✝¹⁷ : OpensMeasurableSpace β
inst✝¹⁶ : TopologicalSpace γ
inst✝¹⁵ : MeasurableSpace γ
inst✝¹⁴ : BorelSpace γ
inst✝¹³ : TopologicalSpace γ₂
inst✝¹² : MeasurableSpace γ₂
inst✝¹¹ : BorelSpace γ₂
inst✝¹⁰ : MeasurableSpace δ
α' : Type ?u.676853
inst✝⁹ : TopologicalSpace α'
inst✝⁸ : MeasurableSpace α'
inst✝⁷ : LinearOrder α✝
inst✝⁶ : OrderClosedTopology α✝
a b x : α✝
α : Type u_1
inst✝⁵ : TopologicalSpace α
m : MeasurableSpace α
inst✝⁴ : SecondCountableTopology α
inst✝³ : LinearOrder α
inst✝² : OrderTopology α
inst✝¹ : BorelSpace α
μ ν : Measure α
inst✝ : IsFiniteMeasure μ
hμν : ↑↑μ univ = ↑↑ν univ
h : ∀ ⦃a b : α⦄, a < b → ↑↑μ (Ico a b) = ↑↑ν (Ico a b)
⊢ ∀ (s : Set α), s ∈ {S | ∃ l u, l < u ∧ Ico l u = S} → ↑↑μ s = ↑↑ν s

tactic: exact h hlt
state_before: case intro.intro.intro
α✝ : Type ?u.676748
β : Type ?u.676751
γ : Type ?u.676754
γ₂ : Type ?u.676757
δ : Type ?u.676760
ι : Sort y
s t u : Set α✝
inst✝²² : TopologicalSpace α✝
inst✝²¹ : MeasurableSpace α✝
inst✝²⁰ : OpensMeasurableSpace α✝
inst✝¹⁹ : TopologicalSpace β
inst✝¹⁸ : MeasurableSpace β
inst✝¹⁷ : OpensMeasurableSpace β
inst✝¹⁶ : TopologicalSpace γ
inst✝¹⁵ : MeasurableSpace γ
inst✝¹⁴ : BorelSpace γ
inst✝¹³ : TopologicalSpace γ₂
inst✝¹² : MeasurableSpace γ₂
inst✝¹¹ : BorelSpace γ₂
inst✝¹⁰ : MeasurableSpace δ
α' : Type ?u.676853
inst✝⁹ : TopologicalSpace α'
inst✝⁸ : MeasurableSpace α'
inst✝⁷ : LinearOrder α✝
inst✝⁶ : OrderClosedTopology α✝
a✝ b✝ x : α✝
α : Type u_1
inst✝⁵ : TopologicalSpace α
m : MeasurableSpace α
inst✝⁴ : SecondCountableTopology α
inst✝³ : LinearOrder α
inst✝² : OrderTopology α
inst✝¹ : BorelSpace α
μ ν : Measure α
inst✝ : IsFiniteMeasure μ
hμν : ↑↑μ univ = ↑↑ν univ
h : ∀ ⦃a b : α⦄, a < b → ↑↑μ (Ico a b) = ↑↑ν (Ico a b)
a b : α
hlt : a < b
⊢ ↑↑μ (Ico a b) = ↑↑ν (Ico a b)