∀ {V : Type u_1} {G : SimpleGraph V} {v w v' w' : V} {p₁ : G.Walk v w} {p₂ : G.Walk v' w'}
  (motive : p₁.support <:+: p₂.support → Prop) (x : p₁.support <:+: p₂.support),
  (∀ (s t : List V) (h : s ++ p₁.support ++ t = p₂.support), motive ⋯) → motive x