reserve x,y for Real;
reserve a,b,c for Element of Real_Lattice;
reserve p,q,r for Element of Real_Lattice;

theorem Th1:
  maxreal.(p,q) = maxreal.(q,p)
proof
  thus maxreal.(p,q) = q"\/"p by LATTICES:def 1
    .= maxreal.(q,p);
end;
