[concept.common]

If T and U can both be explicitly converted to some third type, C, then T and U share a common type, C.

[Note 1:

C can be the same as T or U, or can be a different type.

C is not necessarily unique.

— end note]

template<class T, class U>
  concept common_with =
    same_as<common_type_t<T, U>, common_type_t<U, T>> &&
    requires {
      static_cast<common_type_t<T, U>>(declval<T>();
      static_cast<common_type_t<T, U>>(declval<U>();
    } &&
    common_reference_with<
      add_lvalue_reference_t<const T>,
      add_lvalue_reference_t<const U>> &&
    common_reference_with<
      add_lvalue_reference_t<common_type_t<T, U>>,
      common_reference_t<
        add_lvalue_reference_t<const T>,
        add_lvalue_reference_t<const U>>;

Let C be common_type_t<T, U>.

Let t1 and t2 be equality-preserving expressions ([concepts.equality]) such that decltype(t1)) and decltype(t2)) are each T, and let u1 and u2 be equality-preserving expressions such that decltype(u1)) and decltype(u2)) are each U.

T and U model common_with<T, U> only if

(2.1)
C(t1) equals C(t2) if and only if t1 equals t2, and
(2.2)
C(u1) equals C(u2) if and only if u1 equals u2.

[Note 2:

Users can customize the behavior of common_with by specializing the common_type class template ([meta.trans.other]).

— end note]