theorem Th43: :: GLIB_008:43

for G2 being _Graph
for v1, v2 being Vertex of G2
for e being object
for G1 being addEdge of G2,v1,e,v2
for w being Vertex of G1
for v being Vertex of G2 st not e in the_Edges_of G2 & v = w & not v in G2 .reachableFrom v1 & not v in G2 .reachableFrom v2 holds
G1 .reachableFrom w = G2 .reachableFrom v