reserve G for _Graph;
reserve V for non empty set, E for Relation of V;

theorem Th64:
  for e,v,w being object st e DJoins v,w,createGraph(V,E) holds e = [v,w]
proof
  let e,v,w be object;
  assume A1: e DJoins v,w,createGraph(V,E);
  then e in the_Edges_of createGraph(V,E) by GLIB_000:def 14;
  then A2: e in E;
  then consider v1,w1 being object such that
    A3: e = [v1,w1] by RELAT_1:def 1;
  e DJoins v1,w1,createGraph(V,E) by A2, A3, Th63;
  then v1 = v & w1 = w by A1, GLIB_000:125;
  hence thesis by A3;
end;
