for G2 being _Graph
for v1, v2 being Vertex of G2
for e being object
for G1 being addEdge of G2,v1,e,v2 st not e in the_Edges_of G2 & ( for v3, v4 being Vertex of G2 holds
( v3,v4 are_adjacent or v3 = v4 or ( v1 = v3 & v2 = v4 ) or ( v1 = v4 & v2 = v3 ) ) ) holds
G1 is complete