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 Th33:
  b is_a_fixpoint_of f implies
  ex a st a in dom criticals f & b = (criticals f).a
  proof
    set X = {a where a is Element of dom f: a is_a_fixpoint_of f};
    assume
A1: b is_a_fixpoint_of f;
    b in X by A1; then
    b in rng criticals f by Th30; then
    ex x being object st x in dom criticals f & b = (criticals f).x
by FUNCT_1:def 3;
    hence thesis;
  end;
