theorem Th38: :: MESFUN16:38

for x being Element of REAL
for f being PartFunc of [:RNS_Real,RNS_Real:],RNS_Real
for g being PartFunc of [:REAL,REAL:],REAL
for Pg1 being PartFunc of REAL,REAL st f is_continuous_on dom f & f = g & Pg1 = ProjPMap1 (|.(R_EAL g).|,x) holds
Pg1 is continuous