I am conclusively shown to be better (8)
I believe the answer is:
improved
'be better' is the definition.
(similar in meaning)
'i am conclusively shown' is the wordplay.
'i am' becomes 'I'm' (contraction).
'conclusively shown' becomes 'proved'.
'im'+'proved'='IMPROVED'
'to' acts as a link.
(Other definitions for improved that I've seen before include "Made or got better" , "Became better" , "Made progress" , "Grew or made better" , "Made better in quality" .)