have IHα := freshVarProg_is_larger α
α : Program
φ : Formula
IHφ : ∀ n ∈ voc φ, n < freshVarForm φ
⊢ ∀ (n : ℕ), n ∈ vocabOfProgram α ∨ n ∈ vocabOfFormula φ → n < freshVarProg α ∨ n < freshVarForm φ
α : Program
φ : Formula
IHφ : ∀ n ∈ voc φ, n < freshVarForm φ
IHα : ∀ n ∈ voc α, n < freshVarProg α
⊢ ∀ (n : ℕ), n ∈ vocabOfProgram α ∨ n ∈ vocabOfFormula φ → n < freshVarProg α ∨ n < freshVarForm φ