Macroscopic field as average of microscopic field.(duplicate)

This question has a duplicate but it didn’t answer my doubt. I want to know how in Griffith electrodynamics book there is a portion of field inside dielectric where it says the expression we have been using is the average potential of microscopic properties to get the macroscopic summary of the field.
But i was unable to understand how is the proof done. I have seen some resources on net but unable to understand none.
I could only understand how the expression of E(ave out) and E(ave inside) comes but how does it proves that the expression we have been using is the average i could not understand any argument on any resources i have seen.
How does their sum go to complete volume of space i am unable to understand as it’s for a small region only and how does it relates to the potential expression. If there’s any alternative derivation also i shall be interested to know.
Please help me. I know that this same question is here in stack exchange but i couldn’t understand the answer and my doubt is a bit wide as i am unable to understand anything of the proof while in the other question it seems the OP was able to get the feel of proof that i am completely unable.
Please it’s a request.