cases α
α : Program
⊢ ∀ n ∈ voc α, n < freshVarProg α
case atom_prog
a✝ : ℕ
⊢ ∀ n ∈ voc (·a✝), n < freshVarProg (·a✝)

case sequence
a✝¹ a✝ : Program
⊢ ∀ n ∈ voc (a✝¹;'a✝), n < freshVarProg (a✝¹;'a✝)

case union
a✝¹ a✝ : Program
⊢ ∀ n ∈ voc (a✝¹⋓a✝), n < freshVarProg (a✝¹⋓a✝)

case star
a✝ : Program
⊢ ∀ n ∈ voc (∗a✝), n < freshVarProg (∗a✝)

case test
a✝ : Formula
⊢ ∀ n ∈ voc (?'a✝), n < freshVarProg (?'a✝)