establish

3. VERB

If you establish that something is true, you discover facts that show that it is definitely true.[ FORMAL ]     

• Medical tests established that she was not their own child.     
• It will be essential to establish how the money is being spent.     
• An autopsy was being done to establish the cause of death.     
• It was established that the missile had landed on a test range in Australia.     
• = ascertain    
• established ADJ : usu ADJ n :  That link is an established medical fact.

..... cobuild

3. To cause to be recognized and accepted: 

• a discovery that established his reputation.
  

5. To prove the validity or truth of: 

• The defense attorneys established the innocence of the accused.
  

....... Am-Heritage