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5 hours ago comment added user14111 I guess there is a difference between "(X proved $P(n)$) for infinitely many $n$" and "X proved ($P(n)$ for infinitely many $n$)".
5 hours ago comment added user14111 If X proved that $P(n)\implies Q(n)$, and if it is "likely but not proved" that $P(n)$ holds for infinitely many $n$, is it then "likely but not proved" that X established $Q(n)$ for infinitely many $n$? Consider the degenerate case $P(n)=Q(n)$.
6 hours ago history answered Alexandre Eremenko CC BY-SA 4.0