theorem Th158: :: GLCOLO00:158

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 t1 being TColoring of G1
for t2 being TColoring of G2
for x, y being object st not e in the_Edges_of G2 & not v in the_Vertices_of G2 & t1 _V = (t2 _V) +* (v .--> x) & t1 _E = (t2 _E) +* (e .--> y) & not y in (rng (t2 _V)) \/ (rng (t2 _E)) & x <> y & x <> (t2 _V) . w & t2 is proper holds
t1 is proper