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> > "If X is greater than 10, X is greater than 20" theorems

I think I have seen theorems of that sort. (Can't think of a specific example right now.)

A theorem like that isn't provable (unless you're using some kind of nonstandard arithmetic).

You could only prove it if you add something else, e.g. a precondition saying that X = 30.

Right, if it can be asserted based on some independent assumptions that a positive X must be at least 30, then from those assumptions and X > 10 it would follow that X > 20.

It also just follows from X being >= 30.

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