
theorem Th83:
  for G1 being _Graph, E being set, G2 being reverseEdgeDirections of G1, E
  ex F being PGraphMapping of G1, G2 st F = id G1 & F is isomorphism
proof
  let G1 be _Graph, E be set, G2 be reverseEdgeDirections of G1, E;
  reconsider F = id G1 as PGraphMapping of G1, G2 by GLIB_010:12;
  take F;
  thus F = id G1;
  dom F_V = the_Vertices_of G1 & dom F_E = the_Edges_of G1;
  then A1: F is total by GLIB_010:def 11;
  rng F_V = the_Vertices_of G2 & rng F_E = the_Edges_of G2 by GLIB_007:4;
  then A2: F is onto by GLIB_010:def 12;
  F_V is one-to-one & F_E is one-to-one;
  then F is one-to-one by GLIB_010:def 13;
  hence F is isomorphism by A1, A2;
end;
