for G2 being _Graph
for v being object
for V being set
for G1 being addAdjVertexToAll of G2,v,V st V c= the_Vertices_of G2 & not v in the_Vertices_of G2 holds
for e, v1, v2 being object st v1 <> v & e DJoins v1,v2,G1 holds
e DJoins v1,v2,G2