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How does sinning in Moshe's lifetime prove that they will sin after his death? And how could Moshe know something that depends on free choice?
1.
Kol Eliyahu and Divrei Eliyahu: Some fathers punish their children immediately for anything wrong, and others wait until their measure [of sin] is full. The punishment has greater effect on the former. In Moshe's lifetime, Hashem punished immediately - like we find after the sin of the Golden Calf, by the complainers and by Korach. After his death, Hashem will punish only once in a while - "be'Acharis ha'Yamim" (Pasuk 29) - all the more so they will sin! 1
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It was a Kal va'Chomer, not a prophecy (PF).
