theorem Th155: :: GLCOLO00:155

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