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.

Theorem abs_round_le_generic :
forall x y, generic_format y -> (Rabs x <= y)%R -> (Rabs (round rnd x) <= y)%R.