injection heq₂ with heq₂
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 : j + 1 = Nat.succ j'
⊢ f ∈
    let prev := lindenbaumSequence t Δ (i', j');
    let l := (Denumerable.ofNat (Form × Form) j').fst;
    let r := (Denumerable.ofNat (Form × Form) j').snd;
    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'
⊢ f ∈
    let prev := lindenbaumSequence t Δ (i', j');
    let l := (Denumerable.ofNat (Form × Form) j').fst;
    let r := (Denumerable.ofNat (Form × Form) j').snd;
    if l¦r ∈ ▲prev then if ▲(prev ∪ {l}) ∩ Δ = ∅ then prev ∪ {l} else prev ∪ {r} else prev