replace (a - (a - S n)) with (S a - S (a - S n)).
rewrite <- (minus_Sn_m a (S (a - S n))). rewrite (minus_Sn_m a (S n)).
simpl in |- *. rewrite <- H. rewrite H. rewrite H. trivial with arith.
apply le_Sn_le. exact H0.
apply le_Sn_le. exact H0. apply le_Sn_le. exact H0. exact H0.
rewrite minus_Sn_m. simpl in |- *. apply minus_le_lem2. exact H0. simpl in |- *. trivial with arith.
Qed.

Lemma le_minus_minus : forall a b c : nat, c <= b -> a - b <= a - c.
simple induction a. simpl in |- *. auto with arith.