reserve G, G2 for _Graph, V, E for set,
  v for object;

theorem Th26:
  for G2 for G1 being reverseEdgeDirections of G2
  holds the_Source_of G1 = the_Target_of G2 &
    the_Target_of G1 = the_Source_of G2
proof
  let G2;
  let G1 be reverseEdgeDirections of G2;
  A1: dom the_Target_of G2 = the_Edges_of G2 &
    dom the_Source_of G2 = the_Edges_of G2 by FUNCT_2:def 1;
  thus the_Source_of G1 = the_Source_of G2 +* (
      (the_Target_of G2) | the_Edges_of G2) by Def1
    .= the_Target_of G2 by A1, FUNCT_4:19;
  thus the_Target_of G1 = the_Target_of G2 +* (
      (the_Source_of G2) | the_Edges_of G2) by Def1
    .= the_Source_of G2 by A1, FUNCT_4:19;
end;
