ops.cpp

namespace ops {
    struct gatekeeper {};

    template<typename T>
    bool operator>(T const &a, T const &b) {
        return b < a;
    }

    template<typename T>
    bool operator==(T const &a, T const &b) {
        return !(a < b) && !(b < a);
    }

    // ...
}

struct my_struct : private ops::gatekeeper {
    int a;
    my_struct(int a) : a{a} {}

    bool operator<(my_struct const& other) const {
        return a < other.a;
    }

    bool operator==(my_struct const& other) const {
        return a == other.a;
    }
};

void test(my_struct s1, my_struct s2) {
    s1 < s2;
    s1 > s2;
    s1 == s2;
}