have IHα := freshVarProg_is_larger α
α β : Program
⊢ ∀ (n : ℕ), n ∈ vocabOfProgram α ∨ n ∈ vocabOfProgram β → n < freshVarProg α ∨ n < freshVarProg β
α β : Program
IHα : ∀ n ∈ voc α, n < freshVarProg α
⊢ ∀ (n : ℕ), n ∈ vocabOfProgram α ∨ n ∈ vocabOfProgram β → n < freshVarProg α ∨ n < freshVarProg β