Sentence & direct product

You can find this here:
http://www.thoralf.uwaterloo.ca/htdocs/UALG/univ-algebra.pdf
page 235 (251 in Adobe Reader), def. 2.4.


"If (A*_i)_{i \in I} is a nonempty indexed family of structures of type L
and if F(a_1,...,a_n) is a sentence of type L_a, where
    __
A=  ||    A_i
  i \in I      ... "

[CUT]




Here in F(a_1,...,a_n)  we mean (as far as I know) that a_i (for each i) is
a sequence (a pair, a 7-tuple, a j-tuple ecc...)
Could someone give me a concrete example of sentence like F(a_1,...,a_n)
(assume I={1,2,3} for example, you are free to choose the A_i sets).
Thank you.