induction a
Γ : Type
inst✝ : Alphabet Γ
a : (Term.algebra (RankedAlphabet.lift Γ) Empty).carrier
⊢ ∃ a_1, treeₑ a_1 = a
case var
Γ : Type
inst✝ : Alphabet Γ
h✝ : Empty
⊢ ∃ a, treeₑ a = var h✝

case app
Γ : Type
inst✝ : Alphabet Γ
σ✝ : (RankedAlphabet.lift Γ).alphabet
v✝ : Fin (RankedAlphabet.rank (RankedAlphabet.lift Γ) σ✝) → Term (RankedAlphabet.lift Γ) Empty
v_ih✝ : ∀ (a : Fin (RankedAlphabet.rank (RankedAlphabet.lift Γ) σ✝)), ∃ a_1, treeₑ a_1 = v✝ a
⊢ ∃ a, treeₑ a = app σ✝ v✝