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pfaffelh
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Mathlib/MeasureTheory/Constructions/Cylinders.lean

Lines changed: 3 additions & 3 deletions
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@@ -120,15 +120,15 @@ theorem isPiSystem_squareCylinders [∀ i, Inhabited (α i)] {C : ∀ i, Set (Se
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· simp only [h, Finset.piecewise_eq_of_mem, t₁']
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exact h₁ i
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· simp only [t₁']
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rw [Finset.piecewise_eq_of_not_mem s₁ t₁ (fun i ↦ univ) h]
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rw [Finset.piecewise_eq_of_notMem s₁ t₁ (fun i ↦ univ) h]
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exact hC_univ i
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let t₂' := s₂.piecewise t₂ (fun i ↦ univ)
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have ht₂ (i : ι) : t₂' i ∈ C i := by
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by_cases h : i ∈ s₂
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· simp only [h, Finset.piecewise_eq_of_mem, t₂']
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exact h₂ i
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· simp only [t₂']
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rw [Finset.piecewise_eq_of_not_mem s₂ t₂ (fun i ↦ univ) h]
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rw [Finset.piecewise_eq_of_notMem s₂ t₂ (fun i ↦ univ) h]
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exact hC_univ i
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have h₁ : (s₁ : Set ι).pi t₁' = (s₁ : Set ι).pi t₁ := by
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refine Set.pi_congr rfl ?_
@@ -140,7 +140,7 @@ theorem isPiSystem_squareCylinders [∀ i, Inhabited (α i)] {C : ∀ i, Set (Se
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(fun i ↦ t₁' i ∩ t₂' i) := by
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rw [squareCylinder, squareCylinder, squareCylinder, Finset.coe_union, union_pi_inter, h₁, h₂]
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<;>
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exact fun i a ↦ Finset.piecewise_eq_of_not_mem _ _ (fun i ↦ Set.univ) a
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exact fun i a ↦ Finset.piecewise_eq_of_notMem _ _ (fun i ↦ Set.univ) a
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rw [h] at hst_nonempty ⊢
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rw [squareCylinder, squareCylinders_eq_iUnion_image' C, mem_iUnion]
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· use (s₁ ∪ s₂), (fun i ↦ t₁' i ∩ t₂' i)

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