Can a corollary follow a conjecture? It is typical to find a corollary that following theorems, but is it right to use the word corollary for a statement following a conjecture, where the statement is true only if the unproven conjecture is true?
 A: I would write "Proposition Z: If X holds, then Y is true." Even if the deduction of 
Y from X were trivial, I think labelling this a corollary would be confusing. (After all,
what is the statement "X implies Y" a corollary of?) However, I wouldn't have a 
problem writing something like "as we saw above, Y would be a corollary of X" later on. (The subjunctive voice is important here!)
A: Making a new Theorem environment that let you have the bolded part say "Corollary to Conjecture X" seems to me a good compromise of concise and unlikely to confuse anyone.
A: The correct term for such an item is CONJOLLARY.
;)
A: I think it's generally bad form to have a corollary dependent on an earlier conjecture.  I recommend one of the following:
Theorem:  Assuming Conjecture A, properties X, Y and Z are true.
or 
Theorem:  Conjecture A implies X, Y and Z.
Most importantly, it should be crystal clear that the result is dependent on the conjecture.
A: I'm reminded of the following story that I posted on my personal web journal a couple years ago:

At the Topology seminar yesterday, the speaker presented a theorem, which he immediately followed with a refinement: a statement that directly and obviously implies the theorem. He labeled his refinement a "corollary". I turned to Noah Snyder, and said that it was more an "uncorollary, or an anticorollary", but as soon as I said as much, the two of us simultaneously correctly labeled the refinement as a "rollary".
There should be more rollaries in mathematical writing.

