rattac.
unfold ratSubtract in *.
rattac.
arithNormalize.
rewrite <- NPeano.Nat.add_sub_swap.
eapply minus_eq_compat.
rewrite minus_add_assoc.
rewrite plus_comm.
rewrite <- minus_add_assoc.
rewrite <- plus_0_r at 1.
apply plus_eq_compat.
do 4 arithSimplify.
symmetry.
eapply minus_diag_eq.
do 4 arithSimplify.
apply le_eq.
do 5 arithSimplify.
do 4 (apply mult_le_compat; trivial).
do 4 arithSimplify.
do 4 (apply mult_le_compat; trivial).
Qed.

Lemma ratAdd_any_leRat_l : forall r1 r2 r3,
r1 <= r3 ->
r1 <= r3 + r2.