(** With the current convention, the following result isn't always true with a negative last divisor. For instance [ 3/(-2)/(-2) = 1 <> 0 = 3 / (-2*-2) ], or [ 5/2/(-2) = -1 <> -2 = 5 / (2*-2) ]. *)

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