theorem Th39: :: MESFUN16:39

for y being Element of REAL
for f being PartFunc of [:RNS_Real,RNS_Real:],RNS_Real
for g being PartFunc of [:REAL,REAL:],REAL
for p2 being PartFunc of REAL,REAL st f is_continuous_on dom f & f = g & p2 = ProjPMap2 (|.(R_EAL g).|,y) holds
p2 is continuous