C++ friend operator definition inside class body serves as function declaration?

Question

I'm a newbie reading the C++ Primer book. It says:

A friend declaration only specifies access. It is not a general declaration of the function. If we want users of the class to be able to call a friend function, then we must also declare the function separately from the friend declaration. To make a friend visible to users of the class, we usually declare each friend (outside the class) in the same header as the class itself.

But I just found that this is not the case for friend operator functions defined inside the class body. In the following code, f could not be found but operator+ is found:

struct X
{
    friend void f()
    {
        // friend functions can be defined in the class
        // this does NOT serve as a declaration, even though this is already a definition
        // to use this function, another declaration is REQUIRED
    }

    friend X operator+(const X & x1, const X & x2)
    {
        // this stuff serves as declaration somehow
        return {x1.v + x2.v};
    }

    void foo()
    {
        f();                    // ERROR: no declaration for f
        X tmp = X {1} + X {2};  // CORRECT
    }

    int v;
};

Could someone tell me what makes this difference? I am using g++ (Ubuntu 9.3.0-17ubuntu1~20.04) 9.3.0, as a reference. I have searched many questions involving friend declaration and definition on StackOverflow but did not find an answer on this. Sorry if this question is duplicated.

Answer 1

The difference is the operator+ takes X as parameter, then ADL could find the name; f takes nothing, ADL can't help any.

(emphasis mine)

Names introduced by friend declarations within a non-local class X become members of the innermost enclosing namespace of X, but they do not become visible to ordinary name lookup (neither unqualified nor qualified) unless a matching declaration is provided at namespace scope, either before or after the class definition. Such name may be found through ADL which considers both namespaces and classes.