∀ {α : Type u_1} [inst : LT α] [inst_1 : DecidableLT α] [inst_2 : DecidableEq α],
  (∀ (x : α), ¬x < x) →
    (∀ {x y z : α}, x < y → y < z → x < z) →
      (∀ {x y : α}, ¬x < y → ¬y < x → x = y) → Std.TransCmp fun x1 x2 => compareOfLessAndEq x1 x2