Standard notation of proposition in induction?

Question

I am wondering whether the following notation in mathematical induction is standard.

For example, P(k) is a proposition and we write:

$P(k):\sum_{i=1}^{k}F_i^2=F_{k}F_{k+1}.$

Thank you.

Answer 1

There is no standard notation. Yours is clear enough.

Answer 2

There's no canonical choice, but $P$ is usually used to denote a proposition. It's like how $n$ usually denotes a natural number, or $f$ usually represents a function.