cases δ_in
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, ⋯⟩) ∨ δ ∈ P β fun τ => ℓ ⟨↑τ, ⋯⟩
⊢ lengthOfProgram γ < 1 + lengthOfProgram α + lengthOfProgram β
case inl
γ : Program
δ : List Program
γ_in : γ ∈ δ
α β : Program
ℓ : TP (α⋓β)
h✝ : δ ∈ P α fun τ => ℓ ⟨↑τ, ⋯⟩
⊢ lengthOfProgram γ < 1 + lengthOfProgram α + lengthOfProgram β

case inr
γ : Program
δ : List Program
γ_in : γ ∈ δ
α β : Program
ℓ : TP (α⋓β)
h✝ : δ ∈ P β fun τ => ℓ ⟨↑τ, ⋯⟩
⊢ lengthOfProgram γ < 1 + lengthOfProgram α + lengthOfProgram β