(** With the current convention, the following result isn't always true with a negative intermediate divisor. For instance [ 3/(-2)/(-2) = 1 <> 0 = 3 / (-2*-2) ] and [ 3/(-2)/2 = -1 <> 0 = 3 / (-2*2) ]. *)

Lemma div_div : forall a b c, 0<b -> c~=0 ->
(a/b)/c == a/(b*c).