Final answer:
The proof that if (a · b) | c, then a | c, based on the fact that multiplication of integers is closed and thus if a times b is a divisor of c, it implies c is a multiple of a.
Step-by-step explanation:
To prove the statement "if (a · b) | c, then a | c":
We start by understanding what the notation (a · b) | c means. It indicates that a times b is a divisor of c, or there exists an integer k such that c = (a · b) · k. If we rewrite this expression, we get c = a · (b · k). Now, since b · k is an integer (because the set of integers is closed under multiplication), this implies that c is a multiple of a, hence a | c.