intuition.
unfold ratSubtract.
rattac.
arithNormalize.
apply minus_le.
rewrite <- (mult_assoc n).
rewrite (mult_comm x0).
rewrite mult_assoc.
apply mult_le_compat; trivial.
Qed.

Theorem ratDistance_le_trans : forall r1 r2 r3 d1 d2,
ratDistance r1 r2 <= d1 ->
ratDistance r2 r3 <= d2 ->
ratDistance r1 r3 <= d1 + d2.