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