Section NumDomainMonotonyTheoryForReals.
Local Open Scope order_scope.
Variables (R R' : numDomainType) (D : pred R) (f : R -> R') (f' : R -> nat).
Implicit Types (m n p : nat) (x y z : R) (u v w : R').

Lemma real_nmono_in :
{in D &, {homo f : x y /~ x < y}} ->
{in [pred x in D | x \is real] &, {mono f : x y /~ x <= y}}.