On a simple problem due to Yves Bertot

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Starts from Bertot’s puzzle that the product of two consecutive naturals is even and proves the general claim that the product of m consecutive integers is divisible by m!; uses the Rocq proof assistant and its tactic language to formalize “consecutive” and “even” and to write uniform proofs. Examples show 2 → 2, 3 → 6, 4 → 24, 5 → 120 and lead to a nested induction proof that scales; classroom lab scripts compile and the mechanized proofs check and reuse cleanly.

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1. 0:00Talk introduction
2. 1:25Analytical exploration structure
3. 3:30Students' proof skills
4. 6:19Functional programming to proof trees
5. 8:03Isomorphism of types and propositions
6. 9:34Yves Bertot's simple problem
7. 10:39Students' proof strategies
8. 12:05Three consecutive numbers
9. 13:08Induction vs case analysis
10. 14:35m consecutive numbers and factorial
11. 15:58Divisibility and binomial coefficients
12. 17:02Bloom's taxonomy benefits
13. 18:08Why Coq for teaching proofs
14. 20:37LLM limitations in learning
15. 22:04Programming language grammar
16. 23:51Students' feedback and epiphanies
17. 26:19Teaching challenges and solutions
18. 28:51Analytical value in SAS
19. 29:32Teaching in Asia with humor
20. 33:08Teaching polymorphism with a joke
21. 35:23Reproducibility and theater plays
22. 38:05Assessing epiphanies and proof assistants
23. 41:41Voevodsky on Coq proof checking
24. 42:02Meaning of being analytical