theorem Th19: :: MESFUN17:19

for x, y being Element of REAL
for f being PartFunc of [:[:RNS_Real,RNS_Real:],RNS_Real:],RNS_Real
for g being PartFunc of [:[:REAL,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,y]) holds
Pg1 is continuous