intros prev l r
t : Th
Δ : Ctx
b : Lex (ℕ × ℕ)
i j : ℕ
f : Form
h₃ : f ∈ lindenbaumSequence t Δ (i, j)
x✝ : Lex (ℕ × ℕ)
i' j' : ℕ
heq₁ : i = i'
heq₂ : Nat.add j 0 = j'
heq₃ : j = j'
⊢ let prev := lindenbaumSequence t Δ (i, j);
  let l := (Denumerable.ofNat (Form × Form) j).fst;
  let r := (Denumerable.ofNat (Form × Form) j).snd;
  f ∈ if l¦r ∈ ▲prev then if ▲(prev ∪ {l}) ∩ Δ = ∅ then prev ∪ {l} else prev ∪ {r} else prev
t : Th
Δ : Ctx
b : Lex (ℕ × ℕ)
i j : ℕ
f : Form
h₃ : f ∈ lindenbaumSequence t Δ (i, j)
x✝ : Lex (ℕ × ℕ)
i' j' : ℕ
heq₁ : i = i'
heq₂ : Nat.add j 0 = j'
heq₃ : j = j'
prev : Ctx := lindenbaumSequence t Δ (i, j)
l : Form := (Denumerable.ofNat (Form × Form) j).fst
r : Form := (Denumerable.ofNat (Form × Form) j).snd
⊢ f ∈ if l¦r ∈ ▲prev then if ▲(prev ∪ {l}) ∩ Δ = ∅ then prev ∪ {l} else prev ∪ {r} else prev