Module: Mathlib.MeasureTheory.VectorMeasure.BoundedVariation

Goal state before:
pp: case inr.refine_1
α : Type u_1
inst✝⁸ : LinearOrder α
inst✝⁷ : DenselyOrdered α
inst✝⁶ : TopologicalSpace α
inst✝⁵ : OrderTopology α
inst✝⁴ : SecondCountableTopology α
inst✝³ : CompactIccSpace α
hα : MeasurableSpace α
inst✝² : BorelSpace α
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : CompleteSpace E
f : α → E
hf : BoundedVariationOn f univ
h'α : Nonempty α
m : AddContent E {s | ∃ u v, u ≤ v ∧ s = Ioc u v} := AddContent.onIoc (Function.rightLim f)
A : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, ‖m s‖ₑ ≤ hf.measureAux s
B : hα = generateFrom {s | ∃ u v, u ≤ v ∧ s = Ioc u v}
m' : VectorMeasure α E
hm' : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, m' s = m s
h'm' : ∀ (s : Set α), ‖m' s‖ₑ ≤ hf.measureAux s
u v : α
huv : u ≤ v
⊢ m (Ioc u v) = Function.rightLim f v - Function.rightLim f u

pp: case inr.refine_1.a
α : Type u_1
inst✝⁸ : LinearOrder α
inst✝⁷ : DenselyOrdered α
inst✝⁶ : TopologicalSpace α
inst✝⁵ : OrderTopology α
inst✝⁴ : SecondCountableTopology α
inst✝³ : CompactIccSpace α
hα : MeasurableSpace α
inst✝² : BorelSpace α
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : CompleteSpace E
f : α → E
hf : BoundedVariationOn f univ
h'α : Nonempty α
m : AddContent E {s | ∃ u v, u ≤ v ∧ s = Ioc u v} := AddContent.onIoc (Function.rightLim f)
A : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, ‖m s‖ₑ ≤ hf.measureAux s
B : hα = generateFrom {s | ∃ u v, u ≤ v ∧ s = Ioc u v}
m' : VectorMeasure α E
hm' : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, m' s = m s
h'm' : ∀ (s : Set α), ‖m' s‖ₑ ≤ hf.measureAux s
u v : α
huv : u ≤ v
⊢ Ioc u v ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}

Tactic:
]

Goal state after:
case inr.refine_1
α : Type u_1
inst✝⁸ : LinearOrder α
inst✝⁷ : DenselyOrdered α
inst✝⁶ : TopologicalSpace α
inst✝⁵ : OrderTopology α
inst✝⁴ : SecondCountableTopology α
inst✝³ : CompactIccSpace α
hα : MeasurableSpace α
inst✝² : BorelSpace α
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : CompleteSpace E
f : α → E
hf : BoundedVariationOn f univ
h'α : Nonempty α
m : AddContent E {s | ∃ u v, u ≤ v ∧ s = Ioc u v} := AddContent.onIoc (Function.rightLim f)
A : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, ‖m s‖ₑ ≤ hf.measureAux s
B : hα = generateFrom {s | ∃ u v, u ≤ v ∧ s = Ioc u v}
m' : VectorMeasure α E
hm' : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, m' s = m s
h'm' : ∀ (s : Set α), ‖m' s‖ₑ ≤ hf.measureAux s
u v : α
huv : u ≤ v
⊢ m (Ioc u v) = Function.rightLim f v - Function.rightLim f u

case inr.refine_1.a
α : Type u_1
inst✝⁸ : LinearOrder α
inst✝⁷ : DenselyOrdered α
inst✝⁶ : TopologicalSpace α
inst✝⁵ : OrderTopology α
inst✝⁴ : SecondCountableTopology α
inst✝³ : CompactIccSpace α
hα : MeasurableSpace α
inst✝² : BorelSpace α
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : CompleteSpace E
f : α → E
hf : BoundedVariationOn f univ
h'α : Nonempty α
m : AddContent E {s | ∃ u v, u ≤ v ∧ s = Ioc u v} := AddContent.onIoc (Function.rightLim f)
A : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, ‖m s‖ₑ ≤ hf.measureAux s
B : hα = generateFrom {s | ∃ u v, u ≤ v ∧ s = Ioc u v}
m' : VectorMeasure α E
hm' : ∀ s ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}, m' s = m s
h'm' : ∀ (s : Set α), ‖m' s‖ₑ ≤ hf.measureAux s
u v : α
huv : u ≤ v
⊢ Ioc u v ∈ {s | ∃ u v, u ≤ v ∧ s = Ioc u v}