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Christian, what exactly are you looking for? Are you looking for a definition of the term "lay up"? Or are you looking for a rule that makes them legal?
As far as I know, there's no definition of the term "lay up" in any of the rulesets. A lay up is legal because of the way traveling is defined. If you pick up your dribble with one foot on the ground, that foot is your pivot foot. You are allowed by rule to step with the other foot (that's a pivot) and even to lift your pivot foot -- provided that you release the ball on a try or pass before the pivot foot returns to the floor. That's your lay up right there. Catch, step, jump, shoot. All legal.
That should all be described under pivot foot and traveling definitions, whether you're talking about FIBA or NFHS rules.
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