case inl δ_in =>
  have IH := P_goes_down γ_in δ_in
  cases em (isAtomic α) <;> cases em (isStar α)
  all_goals (simp_all;try linarith)
γ : Program
δ : List Program
γ_in : γ ∈ δ
α β : Program
ℓ : TP (α⋓β)
δ_in : δ ∈ P α fun τ => ℓ ⟨↑τ, ⋯⟩
⊢ lengthOfProgram γ < 1 + lengthOfProgram α + lengthOfProgram β
no goals