Section monotone_abs.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.
Proof with auto with typeclass_instances.
intros x y.
apply round_abs_abs...
clear rnd valid_rnd y.
intros rnd' Hrnd y Hy.
apply round_ge_generic...
Qed.
Proof with auto with typeclass_instances.
intros x y.
apply round_abs_abs...
clear rnd valid_rnd x.
intros rnd' Hrnd x Hx.
apply round_le_generic...
Qed.
End monotone_abs.

Theorem round_DN_opp :
forall x,
round Zfloor (-x) = (- round Zceil x)%R.