theorem Th44: :: GLIB_008:44

for G2 being _Graph
for v1, v2 being Vertex of G2
for e being object
for G1 being addEdge of G2,v1,e,v2 st not e in the_Edges_of G2 holds
G1 .componentSet() = ((G2 .componentSet()) \ {(G2 .reachableFrom v1),(G2 .reachableFrom v2)}) \/ {((G2 .reachableFrom v1) \/ (G2 .reachableFrom v2))}