theorem Th3: :: PARTFUN2:3

for C, D, E being non empty set
for f being PartFunc of C,D
for s being PartFunc of D,E
for h being PartFunc of C,E holds
( h = s * f iff ( ( for c being Element of C holds
( c in dom h iff ( c in dom f & f /. c in dom s ) ) ) & ( for c being Element of C st c in dom h holds
h /. c = s /. (f /. c) ) ) )