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 Th37:
  f is normal & union X in dom f & X is non empty &
  (for x st x in X holds x is_a_fixpoint_of f)
  implies union X = f.union X
  proof assume that
A1: f is normal and
A2: union X in dom f & X is non empty and
A3: for x st x in X holds x is_a_fixpoint_of f;
    for x st x in X ex y st x c= y & y in X & y is_a_fixpoint_of f by A3;
    hence thesis by A1,A2,Th36;
  end;
