{G : Type u_1} →
  {X : Type u_2} →
    {ιₚ : Type u_3} →
      {inst : Group G} →
        {inst_1 : MulAction G X} →
          {P : Sort u} →
            {tiles tiles' : ιₚ → DiscreteTiling.Prototile G X} →
              { tiles := tiles } = { tiles := tiles' } → (tiles ≍ tiles' → P) → P