theorem Th31: :: MESFUN16:31

for X, Y being non empty set
for f being PartFunc of [:X,Y:],REAL
for x being Element of X
for y being Element of Y holds
( ProjPMap1 ((R_EAL f),x) = R_EAL (ProjPMap1 (f,x)) & ProjPMap1 (|.(R_EAL f).|,x) = |.(R_EAL (ProjPMap1 (f,x))).| & ProjPMap2 ((R_EAL f),y) = R_EAL (ProjPMap2 (f,y)) & ProjPMap2 (|.(R_EAL f).|,y) = |.(R_EAL (ProjPMap2 (f,y))).| )