theorem :: FUNCT_4:126

for A1, A2 being non empty set
for Y1 being non empty Subset of A1
for Y2 being non empty Subset of A2
for f being PartFunc of [:A1,A1:],A1
for g being PartFunc of [:A2,A2:],A2
for F being PartFunc of [:Y1,Y1:],Y1 st F = f || Y1 holds
for G being PartFunc of [:Y2,Y2:],Y2 st G = g || Y2 holds
|:F,G:| = |:f,g:| || [:Y1,Y2:]