for G3 being _Graph
for v being object
for V being set
for v1 being Vertex of G3
for G1 being addAdjVertexAll of G3,v,V \/ {v1} st V c= the_Vertices_of G3 & not v in the_Vertices_of G3 & not v1 in V holds
ex G2 being addAdjVertexAll of G3,v,V ex e being object st
( not e in the_Edges_of G2 & ( G1 is addEdge of G2,v,e,v1 or G1 is addEdge of G2,v1,e,v ) )