theorem Th57: :: GLIBPRE1:56

for G2 being _Graph
for v being Vertex of G2
for e, w being object
for G1 being addAdjVertex of G2,v,e,w
for v1 being Vertex of G1 st v1 = v & not e in the_Edges_of G2 & not w in the_Vertices_of G2 holds
G1 .reachableFrom v1 = (G2 .reachableFrom v) \/ {w}