Section CPO_THEORY.
#[local] Existing Instance direct_product_of_two_Prosets.
#[local] Existing Instance subProset.
#[local] Existing Instance pi_isProset.
#[local] Existing Instance Scott_topology.
Definition U {D : Type} {PROSET : isProset D} (x : D) : ensemble D :=
fun z : D => ~ z =< x.

Lemma ScottContinuousMap_isMonotonic {D : Type} {D' : Type} {PROSET : isProset D} {PROSET' : isProset D'} (f : D -> D')
(CONTINUIOUS : isContinuous f)
: isMonotonic1 f.