Section ClosedPredicates.
Variable S : {pred V}.
Definition addr_closed := 0 \in S /\ {in S &, forall u v, u + v \in S}.
Definition oppr_closed := {in S, forall u, - u \in S}.
Definition subr_2closed := {in S &, forall u v, u - v \in S}.
Definition zmod_closed := 0 \in S /\ subr_2closed.

Lemma zmod_closedN : zmod_closed -> oppr_closed.