reserve a,b,c,d for Ordinal;
reserve l for non empty limit_ordinal Ordinal;
reserve u for Element of l;
reserve A for non empty Ordinal;
reserve e for Element of A;
reserve X,Y,x,y,z for set;
reserve n,m for Nat;
reserve f for Ordinal-Sequence;
reserve U,W for Universe;
reserve F,phi for normal Ordinal-Sequence of W;
reserve g for Ordinal-Sequence-valued Sequence;

theorem Th46:
  for g holds
  {a where a is Element of dom(g.0): a in dom(g.0) &
  for f st f in rng g holds a is_a_fixpoint_of f} is ordinal-membered
  proof let g;
    now let x;
      assume x in {a where a is Element of dom(g.0): a in dom(g.0) &
      for f st f in rng g holds a is_a_fixpoint_of f};
      then ex a being Element of dom(g.0) st x = a & a in dom(g.0) &
      for f st f in rng g holds a is_a_fixpoint_of f;
      hence x is ordinal;
    end;
    hence thesis by Th1;
  end;
