reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;
reserve r1,p,p1,g,g1,g2 for Real,
  Y for Subset of REAL;

theorem
  [\ r /] = [/ r \] iff r is integer
proof
  now
    assume
A2: not r is Integer;
    then [\ r /] < r by Th26;
    hence [\ r /] <> [/ r \] by A2,Th31;
  end;
  hence thesis;
end;
