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.
(** Triangular inequality *)

Lemma abs_sub_triangle : forall n m, abs n - abs m <= abs (n-m).