Section div_mult.
Variable (p q : nat) (Hp : p <> 0) (Hq : q <> 0).
Fact div_rem_mult n : div n (p*q) = div (div n p) q /\ rem n (p*q) = rem n p + p*rem (div n p) q.

Corollary div_mult n : div n (p*q) = div (div n p) q.