To-infinitive expressing a result.

As we look back, we can indeed see the the notion of individual rights broadening out to include more and more of the people, until it came at length to be extended to them all.
It was the great message of the French Revolution to proclaim the doctrine of the "fights of man" as applying to all men simply because they are men, and not only to some men
because of some special superiority or prestige.

I'd like to know whether I can think that "to include" expresses the result of "to broaden out" with playing the role of modifying "broadening out", and therefore that "to include" modifies "broadening out" and "broadening out" modifies "the notion."

Thank you, in advance, for your help.