BIP 113 - monotonic guarantee BIP 113 mentions:


  Existing consensus rules guarantee this value to monotonically advance, thereby removing the capability for miners to claim more transaction fees by lying about the timestamps of their block. 


Can you please explain where this guarantee comes from?
The guarantee comes from the consensus rule that a block's timestamp must be greater than the median timestamp of the last 11 blocks. This median timestamp is known as the median time of the block. Because the median is used, and because timestamps of each block must be greater than their median time, the median time will always increase from block to block. This also means that the median time for a block is set prior to it being mined.