theorem Th165: :: GLIB_010:165

for G1, G2 being _Graph
for G3 being removeLoops of G1
for G4 being removeLoops of G2
for F0 being one-to-one PGraphMapping of G1,G2 ex F being one-to-one PGraphMapping of G3,G4 st
( F = F0 | G3 & ( F0 is weak_SG-embedding implies F is weak_SG-embedding ) & ( F0 is isomorphism implies F is isomorphism ) & ( F0 is Disomorphism implies F is Disomorphism ) )