for G3, G4 being _Graph
for v1, v2 being object
for G1 being addVertex of G3,v1
for G2 being addVertex of G4,v2
for F0 being PGraphMapping of G3,G4 st not v1 in the_Vertices_of G3 & not v2 in the_Vertices_of G4 holds
ex F being PGraphMapping of G1,G2 st
( F = [((F0 _V) +* (v1 .--> v2)),(F0 _E)] & ( F0 is total implies F is total ) & ( F0 is onto implies F is onto ) & ( F0 is one-to-one implies F is one-to-one ) & ( F0 is directed implies F is directed ) & ( F0 is semi-continuous implies F is semi-continuous ) & ( F0 is continuous implies F is continuous ) & ( F0 is semi-Dcontinuous implies F is semi-Dcontinuous ) & ( F0 is Dcontinuous implies F is Dcontinuous ) )