
theorem
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  for v being Vertex of G1 st F is isomorphism
  holds F_E.:(v.edgesInOut()) = (F_V/.v).edgesInOut()
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  let v be Vertex of G1;
  assume A1: F is isomorphism;
  then dom F_V = the_Vertices_of G1 by GLIB_010:def 11;
  hence thesis by A1, Th88;
end;
