Section groups.
Variable S : Set.
Variable G : S -> Prop.
Variable Add : S -> S -> S.
Variable O : S.
Variable Opp : S -> S.
(*****************************************************************************)
(*****************)
Definition is_group :=
intern S G Add /\
associativity S Add /\ neutral S G Add O /\ opposite S G Add O Opp.

(****************)
Lemma opp_unicity :
is_group -> forall x y : S, is_opposite S G Add O x y -> y = Opp x.