simp_all
case intro.intro
γ α β : Program
ℓ : TP (α;'β)
αs : List Program
αs_in : αs ∈ List.filter (fun x => x != []) (P α fun τ => ℓ ⟨↑τ, ⋯⟩)
γ_in : γ ∈ αs ++ [β]
⊢ lengthOfProgram γ < 1 + lengthOfProgram α + lengthOfProgram β
case intro.intro
γ α β : Program
ℓ : TP (α;'β)
αs : List Program
αs_in : αs ∈ List.filter (fun x => x != []) (P α fun τ => ℓ ⟨↑τ, ⋯⟩)
γ_in : γ ∈ αs ∨ γ = β
⊢ lengthOfProgram γ < 1 + lengthOfProgram α + lengthOfProgram β