theorem Th141: :: GLIB_010:141

for G1, G2 being _Graph
for E1, E2 being set
for G3 being reverseEdgeDirections of G1,E1
for G4 being reverseEdgeDirections of G2,E2
for F0 being PGraphMapping of G1,G2 ex F being PGraphMapping of G3,G4 st
( F = F0 & ( not F0 is empty implies not F is empty ) & ( 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 semi-continuous implies F is semi-continuous ) & ( F0 is continuous implies F is continuous ) )