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I am using an expression in a paper which doesnt need a proof at all such as $$\sum_{i=k}^K\binom{K}{i}p^i(1-p)^{K-i}$$ is a decreasing function of $k$ and $$\sum_{i=0}^{k-1}\binom{K}{i}p^{K-i}(1-p)^i$$ is an increasing function of $k$. However I connot write it in the text. Because I refer to this property in a non trivial proposition.

Question: How should I put this thing in a format? should I call it as a statement or definition or corollary?

Thank you very much.

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You may not need to make a clearly separated statement, unless it is something that you use a lot. Simply saying, for example, "As $\sum \cdots$ is decreasing wrt $K$..." at the appropriate point(s) will probably suffice. It you do refer to it quite often, either Fact or Observation would work. – arjafi Aug 16 '12 at 10:34
It certainly is not a definition. – Joel Reyes Noche Aug 16 '12 at 10:35
@Joel Reyes Noche and Arthur Fischer thank you very much for your comments. – Seyhmus Güngören Aug 16 '12 at 10:39
up vote 3 down vote accepted

I suggest you use the term Remark.

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