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We pass through another town and a graveyard for children to reach the league. The hall of fame with exhibits for past champions is a neat idea.
Developer laziness completely breaks the game at this point. Once you enter the hall of fame you are locked in. No PC, no x-items, no source of new/different pokemon. If you save here you are stuck until you clear the e4. Defeated e4 trainers do not reset between attempts.
If you reached this point casually, you should consider activating debug mode and giving yourself what you need to win. I did this part legitimately and it took a fair amount of grinding before I could even beat the first trainer.