rattac.
unfold leRat, bleRat in *.
rattac.
arithNormalize.
apply plus_le_compat.
apply mult_le_compat; trivial.
repeat rewrite <- mult_assoc.
repeat rewrite (mult_comm x0).
repeat rewrite mult_assoc.
apply mult_le_compat; trivial.
apply mult_le_compat; trivial.
rewrite <- mult_assoc.
rewrite (mult_comm x1).
rewrite mult_assoc.
apply mult_le_compat; trivial.
Qed.

Theorem ratAdd_leRat_compat : forall r1 r2 r3 r4,
leRat r1 r2 ->
leRat r3 r4 ->
r1 + r3 <= r2 + r4.