Little-O Times Big-O is Little-O/Sequences

Theorem
Let $(a_n),(b_n),(c_n),(d_n)$ be sequences of real or complex numbers.

Let:
 * $a_n = O(b_n)$
 * $c_n = o(d_n)$

where:
 * $O$ denotes big-O notation
 * $o$ denotes little-o notation

Then $a_nc_n = o(b_nd_n)$.