The moral of "The Lion and the Mouse" is "Little friends may prove great friends."

If I say "Little friends may become great friends" instead of the line in bold, will I make a change in meaning? Thanks.

prove: demonstrate, show (implies some testing)
become: evolve to (no testing involved)
It changes the meaning.

In the first, the little friends were always great friends but maybe you didn't realise it.

In the second, the little friends were not great friends initially but became so at some point.
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