reserve L for Lattice,
  p,q,r for Element of L,
  p9,q9,r9 for Element of L.:,
  x, y for set;

theorem Th10:
  for L1,L2 being 1_Lattice st the LattStr of L1 = the LattStr of
  L2 holds Top L1 = Top L2
proof
  let L1,L2 be 1_Lattice;
  assume
A1: the LattStr of L1 = the LattStr of L2;
  then reconsider c = Top L1 as Element of L2;
  now
    let a be Element of L2;
    reconsider b = a as Element of L1 by A1;
    Top L1"\/"b = Top L1;
    hence c"\/"a = c by A1;
    hence a"\/"c = c;
  end;
  hence thesis by LATTICES:def 17;
end;
