18 Concepts library [concepts]

18.5 Comparison concepts [concepts.compare]

18.5.4 Concept totally_­ordered[concept.totallyordered]

```template<class T> concept totally_­ordered = equality_­comparable<T> && partially-ordered-with<T, T>; ```
Given a type T, let a, b, and c be lvalues of type const remove_­reference_­t<T>.
T models totally_­ordered only if
• Exactly one of bool(a < b), bool(a > b), or bool(a == b) is true.
• If bool(a < b) and bool(b < c), then bool(a < c).
• bool(a <= b) == !bool(b < a).
• bool(a >= b) == !bool(a < b).
```template<class T, class U> concept totally_­ordered_­with = totally_­ordered<T> && totally_­ordered<U> && equality_­comparable_­with<T, U> && totally_­ordered< common_reference_t< const remove_reference_t<T>&, const remove_reference_t<U>&>> && partially-ordered-with<T, U>; ```
Given types T and U, let t be an lvalue of type const remove_­reference_­t<T>, u be an lvalue of type const remove_­reference_­t<U>, and C be: common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&> T and U model totally_­ordered_­with<T, U> only if
• bool(t < u) == bool(C(t) < C(u)).
• bool(t > u) == bool(C(t) > C(u)).
• bool(t <= u) == bool(C(t) <= C(u)).
• bool(t >= u) == bool(C(t) >= C(u)).
• bool(u < t) == bool(C(u) < C(t)).
• bool(u > t) == bool(C(u) > C(t)).
• bool(u <= t) == bool(C(u) <= C(t)).
• bool(u >= t) == bool(C(u) >= C(t)).