∀ {K : Type u_1} {Γ : K → Type u_2} {σ : Type u_3} {k : K} (motive : Turing.TM2to1.StAct K Γ σ k → Prop)
  (x : Turing.TM2to1.StAct K Γ σ k),
  (∀ (a : σ → Γ k), motive (Turing.TM2to1.StAct.push a)) →
    (∀ (f : σ → Option (Γ k) → σ), motive (Turing.TM2to1.StAct.peek f)) →
      (∀ (a : σ → Option (Γ k) → σ), motive (Turing.TM2to1.StAct.pop a)) → motive x