∀ {α : Sort u_1} {cmp : α → α → Ordering} [toOrientedCmp : Batteries.OrientedCmp cmp],
  (∀ {x y z : α}, cmp x y ≠ Ordering.gt → cmp y z ≠ Ordering.gt → cmp x z ≠ Ordering.gt) → Batteries.TransCmp cmp