theorem Th62:
  choice_succ_func(w,v,U) is_succ_homomorphism v,w
proof
  set f = choice_succ_func(w,v,U);
  for x st x in LTLNodes(v) & CastNode(x,v) is non elementary & w |= *
CastNode(x,v) holds CastNode(f.x,v) is_succ_of CastNode(x,v) & w |= *CastNode(f
  .x,v)
  proof
    let x such that
A1: x in LTLNodes(v) and
A2: CastNode(x,v) is non elementary & w|=*CastNode(x,v);
    set N = CastNode(x,v);
    set SN = chosen_succ(w,v,U,N);
    CastNode(f.x,v) = CastNode(SN,v) by A1,Def36
      .= SN by Def16;
    hence thesis by A2,Th59;
  end;
  hence thesis;
end;
