for C being non empty set
for c being Element of C
for f1, f2 being PartFunc of C,REAL st f1 is total & f2 is total holds
( (f1 + f2) . c = (f1 . c) + (f2 . c) & (f1 - f2) . c = (f1 . c) - (f2 . c) & (f1 (#) f2) . c = (f1 . c) * (f2 . c) )