A base that reifies as an ordered-carrier subobject Sub(C): it is SetShaped, its carrier is totally ordered (the enabler — so the gate itself, not a later membership call, rejects an unordered carrier), and it coerces to Sub via one of the converting constructors above. The single gate concept for both power_set and 𝔓 (DRY), and — because it conjoins the very SetShaped atom the :sets default is constrained on — it subsumes that deleted gate, so it wins by partial ordering for the ordered families. More...

Concept definition

template<typename S>
concept dedekind::order::SubReifiable = 
    dedekind::sets::SetShaped<S> && IsTotallyOrdered<typename S::Domain> &&
    std::convertible_to<S, Sub<typename S::Domain, typename S::logic_species>>

Detailed Description

A base that reifies as an ordered-carrier subobject Sub(C): it is SetShaped, its carrier is totally ordered (the enabler — so the gate itself, not a later membership call, rejects an unordered carrier), and it coerces to Sub via one of the converting constructors above. The single gate concept for both power_set and 𝔓 (DRY), and — because it conjoins the very SetShaped atom the :sets default is constrained on — it subsumes that deleted gate, so it wins by partial ordering for the ordered families.