Section AbelianGroup1.
Context {G : AbelianGroup}.
Definition zero := AbelianGroup.zero _ (AbelianGroup.class G).
Definition plus := AbelianGroup.plus _ (AbelianGroup.class G).
Definition opp := AbelianGroup.opp _ (AbelianGroup.class G).
Definition minus x y := (plus x (opp y)).

Lemma opp_plus :
forall x y : G,
opp (plus x y) = plus (opp x) (opp y).