Is there a word that encompasses both "definitions" and "theorems"?

Question

I sometimes write sentences like this:

To prove the desired result, the following notions will be handy.

What follows is a usually a sequence of definitions, theorems and proofs. Therefore, I don't think that the word 'notions' really fits, because 'theorems' aren't really 'notions' to my mind.

Question. Is there a word that does fit, which encompasses both definitions and theorems?

Answer 1

"Theory" is theoretically the answer :) Otherwise, settings/framework?

Answer 2

I'd be inclined to say "facts" or "known facts".

A fact might be known because it comes from a definition, or because it comes from a theorem. But, either way, it is "known", and it's a "fact".

Alternatively, you could just refer to definitions and theorems, as in "to prove the following result, we will use the definition given in section (3.5), plus theorems (3.8) and (3.9)".

Or, more briefly: "to prove the following result, we will use (3.5), (3.8), and (3.9)".

Answer 3

I would simply use a slight variation of your sentence:

To prove the desired result, the following notions and facts will be handy.

Not a single word, but short enough.