reserve G for _Graph;
reserve V for non empty set, E for Relation of V;
reserve E for symmetric Relation of V;
reserve G for GraphFromSymRel of V, E;

theorem
  for G1 being non-multi _Graph
  for G2 being GraphFromSymRel of the_Vertices_of G1, VertexAdjSymRel(G1)
  holds G2 is G1-isomorphic
proof
  let G1 be non-multi _Graph;
  let G2 be GraphFromSymRel of the_Vertices_of G1, VertexAdjSymRel(G1);
  consider F being PGraphMapping of G1, G2 such that
    A1: F is isomorphism and F_V = id the_Vertices_of G1 &
      for e being object st e in the_Edges_of G1
      holds F_E.e = [(the_Source_of G1).e,(the_Target_of G1).e] or
        F_E.e = [(the_Target_of G1).e,(the_Source_of G1).e] by Th106;
  thus thesis by A1, GLIB_010:def 23;
end;
