
theorem
  for G1 being _Graph, E being set, G2 being reverseEdgeDirections of G1, E
  holds id G1 = id G2 & id G1 is PGraphMapping of G1, G2
proof
  let G1 be _Graph, E be set;
  let G2 be reverseEdgeDirections of G1, E;
  thus id G1 = [id the_Vertices_of G2, id the_Edges_of G1] by GLIB_007:4
    .= id G2 by GLIB_007:4;
  ex E1, E2 being set st G1 is reverseEdgeDirections of G1, E1
    & G2 is reverseEdgeDirections of G1, E2
  proof
    take {},E;
    thus thesis by GLIB_009:43;
  end;
  hence thesis by Th10;
end;
