theorem
  [/ r \] + i0 = [/ r + i0 \]
proof
  [/ r \] < r + 1 by Def7;
  then [/ r \] + i0 < r + 1 + i0 by XREAL_1:6;
  then
A1: [/ r \] + i0 < r + i0 + 1;
  r <= [/ r \] by Def7;
  then r + i0 <= [/ r \] + i0 by XREAL_1:6;
  hence thesis by A1,Def7;
end;
