theorem :: MONOID_1:46

for D1, D2, D being non empty set
for f being Function of [:D1,D2:],D
for X1 being Subset of D1
for X2 being Subset of D2 holds (f .:^2) . (X1,X2) = { (f . (a,b)) where a is Element of D1, b is Element of D2 : ( a in X1 & b in X2 ) }