for O being set
for G, H being GroupWithOperators of O
for G9 being StableSubgroup of G
for H9 being StableSubgroup of H
for f being Homomorphism of G,H st ( the carrier of H9 = f .: the carrier of G9 or the carrier of G9 = f " the carrier of H9 ) holds
f | the carrier of G9 is Homomorphism of G9,H9