α : Type u
s : Set (Set α)
i : (Quotient.out (ord (aleph 1))).α
f : ℕ → Set α
hf : ∀ (n : ℕ), ∃ j, j < i ∧ f n ∈ generateMeasurableRec s j
⊢ (⋃ (n : ℕ), f n) ∈
    let i := i;
    let S := ⋃ (j : ↑(Iio i)), generateMeasurableRec s ↑j;
    s ∪ {∅} ∪ compl '' S ∪ range fun f => ⋃ (n : ℕ), ↑(f n)
α : Type u
s : Set (Set α)
i : (Quotient.out (ord (aleph 1))).α
f : ℕ → Set α
hf : ∀ (n : ℕ), ∃ j, j < i ∧ f n ∈ generateMeasurableRec s j
⊢ (⋃ (n : ℕ), f n) ∈ generateMeasurableRec s i
unfold generateMeasurableRec
no goals
α : Type u
s : Set (Set α)
i : (Quotient.out (ord (aleph 1))).α
f : ℕ → Set α
hf : ∀ (n : ℕ), ∃ j, j < i ∧ f n ∈ generateMeasurableRec s j
⊢ (⋃ (n : ℕ), f n) ∈
    let i := i;
    let S := ⋃ (j : ↑(Iio i)), generateMeasurableRec s ↑j;
    s ∪ {∅} ∪ compl '' S ∪ range fun f => ⋃ (n : ℕ), ↑(f n)
exact mem_union_right _ ⟨fun n => ⟨f n, let ⟨j, hj, hf⟩ := hf n; mem_iUnion.2 ⟨⟨j, hj⟩, hf⟩⟩, rfl⟩