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

theorem
  for G being non edgeless _Graph, e being Edge of G, H being
    inducedSubgraph of G, {(the_Source_of G).e, (the_Target_of G).e}, {e}
  holds H == createGraph(e)
proof
  let G be non edgeless _Graph, e being Edge of G;
  set V = {(the_Source_of G).e, (the_Target_of G).e};
  let H be inducedSubgraph of G, V, {e};
  (the_Source_of G).e in V & (the_Target_of G).e in V by TARSKI:def 2;
  then A1: {e} c= G.edgesBetween(V) by ZFMISC_1:31, GLIB_000:31;
  the_Vertices_of H = V & the_Edges_of H = {e} by A1, GLIB_000:def 37;
  then the_Vertices_of H = the_Vertices_of createGraph(e) &
    the_Edges_of H = the_Edges_of createGraph(e) by Th13;
  hence thesis by GLIB_000:86;
end;
