for G3 being _Graph
for v1, e being object
for v2 being Vertex of G3
for G2 being addVertex of G3,v1
for G1 being addEdge of G2,v1,e,v2 st not e in the_Edges_of G3 & not v1 in the_Vertices_of G3 holds
G1 is addAdjVertex of G3,v1,e,v2