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 plus_opp_r :
forall x : G,
plus x (opp x) = zero.