intro d d_in
case right
x : ℕ
ψ : Formula
α : Program
δ : List Program
nonOcc : x ∉ vocabOfProgram α ∧ ∀ x_1 ∈ δ, x ∉ vocabOfProgram x_1
⊢ ∀ x_1 ∈ δ, x ∉ vocabOfProgram x_1
case right
x : ℕ
ψ : Formula
α : Program
δ : List Program
nonOcc : x ∉ vocabOfProgram α ∧ ∀ x_1 ∈ δ, x ∉ vocabOfProgram x_1
d : Program
d_in : d ∈ δ
⊢ x ∉ vocabOfProgram d