theorem Th20: :: GLCOLO00:20

for G2 being _Graph
for v, w being Vertex of G2
for e being object
for G1 being addEdge of G2,v,e,w
for f1 being VColoring of G1
for f2 being VColoring of G2 st f1 = f2 & v,w are_adjacent & f2 is proper holds
f1 is proper