theorem :: MESFUN17:58

for y being Element of REAL
for I, J, K being non empty closed_interval Subset 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 P2Gz being PartFunc of REAL,REAL st y in J & [:[:I,J:],K:] = dom f & f is_continuous_on [:[:I,J:],K:] & f = g & P2Gz = (ProjPMap2 ((Integral2 (L-Meas,(R_EAL g))),y)) | I holds
P2Gz is continuous