exfalso
case inl
x : ℕ
F : List Formula
δ : List Program
α : Program
x_notin : x ∉ vocabOfProgram α
y : Program
y_in : y ∈ δ
h✝ : F = [] ∧ δ = []
⊢ x ∉ vocabOfProgram y
case inl
x : ℕ
F : List Formula
δ : List Program
α : Program
x_notin : x ∉ vocabOfProgram α
y : Program
y_in : y ∈ δ
h✝ : F = [] ∧ δ = []
⊢ False