{P : TopCat → Prop} →
  {motive : CompHausLike.HasExplicitFiniteCoproducts P → Sort u_1} →
    (t : CompHausLike.HasExplicitFiniteCoproducts P) →
      ((hasProp : ∀ {α : Type w} [Finite α] (X : α → CompHausLike P), CompHausLike.HasExplicitFiniteCoproduct X) →
          motive ⋯) →
        motive t