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Sleep is like a way for the body to repair the damage that was done on the day by detoxification and repairing tissues. And prepare the cells and body for the next day by fueling each tissue, especially brain.
The more micronutrients you get through bioavailable animal foods the faster and more efficiently your body can repair and prepare for the next day. And that will make you sleep faster.
Obviously your body tries to get repair as fast as possible while sleeping, as sleeping is obviously dangerous in evolutionary way (predator can eat you, etc in nature). And the healthier you are the faster you wake up and be conscious again.