lean_workbook_plus_2212

Prove that: 1) $x < \lfloor x \rfloor+1$ 2) $\lceil x \rceil < x+1$ 3) $\lfloor k+x \rfloor = k+\lfloor x \rfloor$ 4) $\lfloor x \rfloor =-\lceil-x \rceil$ as well as $\lceil x \rceil =-\lfloor-x \rceil$