∀ {α : Type u} {cmp : α → α → Ordering} {cut : α → Ordering},
  (∀ {k k' : α}, cut k' = Ordering.lt → cmp k' k = Ordering.lt → cut k = Ordering.lt) →
    (∀ {k k' : α}, cut k' = Ordering.gt → cmp k' k = Ordering.gt → cut k = Ordering.gt) →
      (∀ (k : α) {k' : α}, cut k' = Ordering.eq → cut k = cmp k' k) → Std.Internal.IsStrictCut cmp cut