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Refactor: Explicit set decomposition and fix doc-gen at line 575 #458

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Refactor: Explicit set decomposition and fix doc-gen at line 575 #458

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10 changes: 8 additions & 2 deletions analysis/Analysis/MeasureTheory/Section_1_3_1.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -571,8 +571,14 @@ lemma weightedMeasureSum_eq_of_eq {d k k' : ℕ}
by_cases h1 : atomMembership k k' i₁ i <;> by_cases h2 : atomMembership k k' i₂ i
· simp only [h1, h2, ite_true]
exact atom_pairwiseDisjoint E E' (by trivial : i₁ ∈ Set.univ) (by trivial) hi
· simp only [h1, h2, ite_true]
rw [Set.disjoint_left]; intro _ _; simp
have hEi : E i = ⋃ j ∈ {j | x ∈ A j}, A j := by
ext y
simp only [mem_iUnion, mem_setOf_eq, exists_prop]
constructor
· intro hy
exact ⟨i, ⟨h_Ei_mem_Ai i hy, hy⟩⟩
· rintro ⟨j, hj_cond, hyA⟩
exact (h_Ai_subset_Ei j) hyA
· simp only [h1, h2, ite_true]
rw [Set.disjoint_left]; simp
· simp only [h1, h2]
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