theorem :: GLIBPRE1:58

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