exfalso
γ α : Program
ℓ : TP (∗α)
γ_in : γ ∈ []
δ_in : [] = [] ∨ ∃ a ∈ List.filter (fun x => x != []) (P α fun x => ℓ ⟨↑x, ⋯⟩), a ++ [∗α] = []
⊢ lengthOfProgram γ ≤ 1 + lengthOfProgram α
γ α : Program
ℓ : TP (∗α)
γ_in : γ ∈ []
δ_in : [] = [] ∨ ∃ a ∈ List.filter (fun x => x != []) (P α fun x => ℓ ⟨↑x, ⋯⟩), a ++ [∗α] = []
⊢ False