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;

theorem Th51:
  On U <> {} & On U is limit_ordinal
proof
  card U = On U by Th9;
  hence thesis by Th19;
end;
