let S, T be up-complete Scott TopLattice; for M being Subset of (SCMaps (S,T)) holds "\/" (M,(SCMaps (S,T))) is continuous Function of S,T
let M be Subset of (SCMaps (S,T)); "\/" (M,(SCMaps (S,T))) is continuous Function of S,T
the carrier of (SCMaps (S,T)) c= the carrier of (MonMaps (S,T))
by YELLOW_0:def 13;
then
"\/" (M,(SCMaps (S,T))) in the carrier of (MonMaps (S,T))
;
hence
"\/" (M,(SCMaps (S,T))) is continuous Function of S,T
by WAYBEL10:9, WAYBEL17:def 2; verum