A sleep cycle progresses through the stages of non-REM sleep from light to deep sleep, then reverse back from deep sleep to light sleep, ending with time in REM sleep before starting over in light sleep again.
The statement that as the sleep cycles continue, the proportion of REM (Rapid Eye Movement) sleep in each cycle decreases is false. The sleep cycle has five stages: stages 1-4 and the REM (rapid eye motion) sleep stage.