It is merely a matter of applying an agreed-upon set of rules (for instance, that any thing is equal to itself, or that if something is true for all members of a set of objects, it is true for any one specific object) to a set of agreed-upon structures, such as sets of objects.

ECONOMIST: Just what does it mean to prove something?

They paid their fines and went away, serving their true purpose, which was to be an object lesson to everyone else.

FORBES: A Timely Reminder that MPAA and RIAA Shouldn't Be Trusted with Too Much Enforcement Power

But last week's was an object lesson in how in subsequent discussions of things that aren't true, or are half true, are accepted as facts.

WSJ: Fiction of the EU Summit's Accepted 'Facts'