unfold lindenbaumSequence
t : Th
Δ : Ctx
f : Form
i j : ℕ
prf₃ : BProof (lindenbaumSequence t Δ (i + 1, Encodable.encode (f, f))) (f¦f)
⊢ f ∈ lindenbaumSequence t Δ (i + 1, Encodable.encode (f, f) + 1)
t : Th
Δ : Ctx
f : Form
i j : ℕ
prf₃ : BProof (lindenbaumSequence t Δ (i + 1, Encodable.encode (f, f))) (f¦f)
⊢ f ∈
    let prev := lindenbaumSequence t Δ (Nat.succ (Nat.add i 0), Nat.add (Encodable.encode (f, f)) 0);
    let l := (Denumerable.ofNat (Form × Form) (Nat.add (Encodable.encode (f, f)) 0)).fst;
    let r := (Denumerable.ofNat (Form × Form) (Nat.add (Encodable.encode (f, f)) 0)).snd;
    if l¦r ∈ ▲prev then if ▲(prev ∪ {l}) ∩ Δ = ∅ then prev ∪ {l} else prev ∪ {r} else prev