theorem
  r - 1 < [/ r \] & r < [/ r \] + 1
proof
  r <= [/ r \] by Def7;
  then
A1: r + 0 < [/ r \] + 1 by XREAL_1:8;
  then r + (- 1) < [/ r \] + 1 + (- 1) by XREAL_1:6;
  hence thesis by A1;
end;
