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