simp_all [isAtomic, isStar, P]
case test
γ : Program
δ : List Program
γ_in : γ ∈ δ
a✝ : Formula
ℓ : TP (?'a✝)
δ_in : δ ∈ P (?'a✝) ℓ
⊢ if isAtomic (?'a✝) = true then γ = (?'a✝)
  else
    if isStar (?'a✝) = true then lengthOfProgram γ ≤ lengthOfProgram (?'a✝)
    else lengthOfProgram γ < lengthOfProgram (?'a✝)
case test
γ : Program
δ : List Program
γ_in : γ ∈ δ
a✝ : Formula
ℓ : TP (?'a✝)
δ_in : δ ∈ if ℓ ⟨a✝, ⋯⟩ = true then [[]] else []
⊢ lengthOfProgram γ < 2 + lengthOfFormula a✝