theorem Th37: :: MESFUN16:37

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 Pg2 being PartFunc of REAL,REAL st f is_continuous_on dom f & f = g & Pg2 = ProjPMap2 ((R_EAL g),y) holds
Pg2 is continuous