theorem Th22: :: MESFUN17:22

for I, J being Subset of REAL
for K being non empty closed_interval Subset of REAL
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 x in I & y in J & dom f = [:[:I,J:],K:] & f is_continuous_on [:[:I,J:],K:] & f = g & Pg1 = ProjPMap1 ((R_EAL g),[x,y]) holds
( Pg1 is_integrable_on L-Meas & integral (Pg1,K) = Integral (L-Meas,Pg1) & integral (Pg1,K) = Integral (L-Meas,(ProjPMap1 ((R_EAL g),[x,y]))) & integral (Pg1,K) = (Integral2 (L-Meas,(R_EAL g))) . [x,y] )