reserve G, G1, G2 for _Graph, H for Subgraph of G;

theorem Th13:
  for G being non edgeless _Graph, e being Edge of G
  holds the_Edges_of createGraph(e) = {e} & the_Vertices_of createGraph(e)
    = {(the_Source_of G).e,(the_Target_of G).e}
proof
  let G be non edgeless _Graph, e be Edge of G;
  consider V being non empty Subset of the_Vertices_of G,
    S, T being Function of {e}, V such that
    A1: createGraph(e) = createGraph(V,{e},S,T) &
      {(the_Source_of G).e,(the_Target_of G).e} = V &
      S = e .--> (the_Source_of G).e & T = e .--> (the_Target_of G).e
    by Def4;
  thus thesis by A1;
end;
