theorem :: GLIBPRE1:59

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