predicate lex_minimize(array[int] of var int: o) =
  let {
    var index_set(o): stage
    array[index_set(o)] of var int: best;
  } in if status() = START then
    stage = min(index_set(o))
  else
    if status() = UNSAT then
      if lastval(stage) < l then
        stage = lastval(stage) + 1
      else
        complete()  % we are finished
      endif
    else
      stage = lastval(stage)
      /\ best[stage] = sol(_objective)
    endif
    /\ for(i in min(index_set(o))..stage-1) (
      o[i] = lastval(best[i])
    )
    /\ if status() = SAT then
        o[stage] < sol(_objective)
    endif
    /\ _objective = o[stage]
  endif;