1

I have a few results that I want to write a corollary for, however I don't know where to include this. Should I write it under the last result as "Corollary of results A, B and C" (where C is the last result that we proved)? How is it usually done? (I have only seen corollaries for single results before, never for multiple results at a time, but my corollary follows from results A,B and C together, not just from one of them.)

Thanks

EDIT: Also, how is "corollary" pronounced?

Is Ne
  • 2,668
  • 1
    The usual pronunciation has primary accent on the first syllable and secondary accent on the third, but British pronunciation has just primary accent on the second syllable. – MPW Feb 20 '15 at 12:45
  • 3
    I presume that theorems A, B and C tackle a similar issue. I would suggest putting all of these in one proposition (Proposition: 1. A 2. B 3. C; proof: (...); corollary: (...)). –  Feb 20 '15 at 12:57

1 Answers1

3

It's hard to say without the logic structure of your corollary, but it's usually possible to write something like:

Consider $\spadesuit$. From $A$ we can infer $\clubsuit$ and $B$ yields $\diamondsuit$. This allows us to do $\heartsuit$ which leads to $\blacksquare$ via $C$. Taking all this together allows us to formulate the following corollary:

Corollary 3.14: Lorem ipsum lorem ipsum lorem ipsum lorem ipsum lorem ipsum lorem ipsum lorem ipsum lorem ipsum

If the results are similar enough, then you can combine them in a single result (already mentioned by @Ahmed in the comments). Personally I try to avoid such composites because these never feel clean enough for me. Still, I've seen such with hardly any drawback.

Yet another way is to formulate the corollary so that it is a direct result of $C$, that is, apply $A$ and $B$ in the premise. The disadvantage is that these might be clumsy, especially if $C$ is a rather minor step when compared to $A$ or $B$.

Finally, you could write an explanation or a proof sketch that would remove any doubt as to which results have been used. That sometimes is the best, but when the corollary is not really important it diverges attention and bloats the paper.

I hope this helps $\ddot\smile$

dtldarek
  • 37,381