have l₅ : l = f := by 
  change (Denumerable.ofNat (Form × Form) (Encodable.encode (f, f))).fst = f
  rw [Denumerable.ofNat_encode (f,f)]
t : Th
Δ : Ctx
f : Form
i j : ℕ
prf₃ : BProof (lindenbaumSequence t Δ (i + 1, Encodable.encode (f, f))) (f¦f)
prev : Ctx := lindenbaumSequence t Δ (i + 1, Encodable.encode (f, f))
l : Form := (Denumerable.ofNat (Form × Form) (Encodable.encode (f, f))).fst
r : Form := (Denumerable.ofNat (Form × Form) (Encodable.encode (f, f))).snd
⊢ f ∈ if l¦r ∈ ▲prev then if ▲(prev ∪ {l}) ∩ Δ = ∅ then prev ∪ {l} else prev ∪ {r} else prev
t : Th
Δ : Ctx
f : Form
i j : ℕ
prf₃ : BProof (lindenbaumSequence t Δ (i + 1, Encodable.encode (f, f))) (f¦f)
prev : Ctx := lindenbaumSequence t Δ (i + 1, Encodable.encode (f, f))
l : Form := (Denumerable.ofNat (Form × Form) (Encodable.encode (f, f))).fst
r : Form := (Denumerable.ofNat (Form × Form) (Encodable.encode (f, f))).snd
l₅ : l = f
⊢ f ∈ if l¦r ∈ ▲prev then if ▲(prev ∪ {l}) ∩ Δ = ∅ then prev ∪ {l} else prev ∪ {r} else prev