cases em (δ' = []) <;> simp_all [H, voc,vocabOfListFormula,vocabOfListProgram,vocabOfFormula,vocabOfProgram]
case intro.intro.intro.intro.intro
x : ℕ
F : List Formula
δ : List Program
α : Program
x_notin : x ∉ vocabOfProgram α
y : Formula
y_in : y ∈ F
F' : List Formula
δ' : List Program
Fδ'_in_Hα : (F', δ') ∈ H α
Fδ_in_l : (F, δ) ∈ if δ' = [] then [] else [(F', δ' ++ [∗α])]
IHα : x ∉ voc F' ∧ x ∉ voc δ'
⊢ x ∉ vocabOfFormula y
no goals