
theorem Th5:
  for G being _Graph
  for V being non empty one-to-one ManySortedSet of the_Vertices_of G
  for e,v,w being object st e DJoins v,w,G
  holds e DJoins V.v,V.w,replaceVertices(V)
proof
  let G be _Graph;
  let V be non empty one-to-one ManySortedSet of the_Vertices_of G;
  let e,v,w be object;
  assume A1: e DJoins v,w,G;
  (id the_Edges_of G).e DJoins V.v,V.w,replaceVertices(V) by A1, Th4;
  hence thesis by A1, FUNCT_1:18, GLIB_000:def 14;
end;
