theorem Th94: :: GLCOLO00:94

for G2 being _Graph
for v, e being object
for w being Vertex of G2
for G1 being addAdjVertex of G2,v,e,w
for g1 being EColoring of G1
for g2 being EColoring of G2
for x being object st g1 = g2 +* (e .--> x) & not x in rng g2 & not e in the_Edges_of G2 & not v in the_Vertices_of G2 & g2 is proper holds
g1 is proper