reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;
reserve U1,U2,U for Universe;
reserve u,v for Element of U;

theorem
  A <> {} & A is limit_ordinal & dom L = A & (for B st B in A holds L.B
  = UNIVERSE B) implies UNIVERSE A = Universe_closure Union L by Lm6;
