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Suppose I write down some assumptions...

  1. $a < b$

  2. $b < c$

    ...and deduce some stuff...

  3. $a < c$
  4. $a \neq c$

is there a word that covers both my assumptions, and the things I've deduced?

For example, if my assumptions had no free variables, I'd feel comfortable calling 1 & 2 "axioms" and calling 1 through to 4 "theorems" or "demonstrated theorems."

goblin GONE
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    I think a slang term for the assumptions is the "givens": given conditions (A), (B), ... The text as a whole might be called a "proposition", where it includes what is given and what can be deduced from it. Then the proof is a separate text. – abiessu Sep 25 '13 at 12:18
  • @abiessu, thanks, that sounds reasonable. – goblin GONE Sep 25 '13 at 14:20

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