Note that std::totally_ordered is a concept (this topic is about "C++ 20 Concepts: The Definitive Guide") whereas you're talking about std::partial_ordering which is a class, also introduced in C++ 20.

Specifically these ordering classes are the result of the spaceship operator and the concept doesn't care whether you have a spaceship operator.

<=> spaceship operator: Good article on the C++20 three-way comparison operator: https://devblogs.microsoft.com/cppblog/simplify-your-code-wi...