
theorem Th42:
  for G1, G2 being _Graph st G1 == G2
  holds G2 is reverseEdgeDirections of G1, {}
proof
  let G1, G2 be _Graph;
  assume A1: G1 == G2;
  A2: {} c= the_Edges_of G1 by XBOOLE_1:2;
  A3: the_Source_of G2 = the_Source_of G1 by A1, GLIB_000:def 34
    .= the_Source_of G1 +* ((the_Target_of G1) | {}) by FUNCT_4:21;
  A4: the_Target_of G2 = the_Target_of G1 by A1, GLIB_000:def 34
    .= the_Target_of G1 +* ((the_Source_of G1) | {}) by FUNCT_4:21;
  the_Vertices_of G1 = the_Vertices_of G2 & the_Edges_of G1 = the_Edges_of G2
    by A1, GLIB_000:def 34;
  hence thesis by A2, A3, A4, GLIB_007:def 1;
end;
