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;

theorem Th28:
  On {a where a is Element of dom f: a is_a_fixpoint_of f}
  = {a where a is Element of dom f: a is_a_fixpoint_of f}
  proof
    set X = {a where a is Element of dom f: a is_a_fixpoint_of f};
    now
      let x;
      assume x in X; then
      ex a being Element of dom f st x = a & a is_a_fixpoint_of f;
      hence x is ordinal;
    end; then
    X is ordinal-membered by Th1;
    hence thesis by Th2;
  end;
