Module Type GenericSgn (Import Z : ZDecAxiomsSig')
(Import ZP : ZMulOrderProp Z) <: HasSgn Z.
Definition sgn n :=
match compare 0 n with Eq => 0 | Lt => 1 | Gt => -1 end.

Lemma abs_neq_iff : forall n, abs n == -n <-> n<=0.