You ask:”How do we know awareness does not die when we die?”
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Contemplate what is it that dies? You do not die. 
The body dies. 

Therefore the correct question is: “How do we know awareness does not die when the body dies?”

Contemplate that if ‘you’ know the body dies, that means ‘you’ did not die. 

The Self is eternal.

Even though you may comprehend these words, you must contemplate and vanquish the feeling of mortality.