theorem Th11: :: MESFUN17:11

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