theorem Th93: :: GLCOLO00:93

for G2 being _Graph
for v, e, w being object
for G1 being addEdge 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 e in the_Edges_of G2 & not x in rng g2 & g2 is proper holds
g1 is proper