agg_all_(min(X,W), Goal, min(Min,Witness)) :-
  State = state(X,W,LastMin),
  (  call(Goal),
     arg(1, State, M0),
     M is min(M0,X),
     \+compare(=, M, LastMin),
     nb_setarg(1, State, M),
     nb_setarg(2, State, W),
     nb_setarg(3, State, M),
     fail
  ;
     arg(1, State, Min),
     arg(2, State, Witness),
     nonvar(Min),
     nonvar(Witness)
  ).