Add prime factorization (Factoring.v) and coprimality iff lemmas - #306
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Factoring.v comes from Andres Erbsen's WIP ZmodSqrt branch (andres-erbsen/stdlib@5bd6d0db, theories/ZArith/Factoring.v). It defines the p-adic valuation `val`, the prime-power factorization `ppfactor`, the sorted prime factorization `factor` and Euler's `totient` on positive numbers, all computable, and proves the fundamental theorem of arithmetic together with the induction principles `factor_ind` and `ppfactor_ind`. The two unfinished scratch lemmas of the WIP (`in_ppfactor`, `val_ext`) are left out. Zdivisibility.v gains `Z.coprime_mul_l_iff`, `Z.coprime_mul_r_iff`, `Z.coprime_pow_l_iff`, `Z.coprime_pow_r_iff` and `Z.coprime_prime_prime`, which the same WIP used. The generic list lemmas it needed go to their natural homes: `Forall_repeat` and `repeat_inj` in List.v; `Sorted_repeat`, `StronglySorted_app`, `NoDup_StronglySorted`, `HdRel_map`, `Sorted_map`, `StronglySorted_Permutation_unique` and `Sorted_Permutation_unique` in Sorted.v (which now requires Permutation); `fold_right_Permutation` in Permutation.v. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01YJbiRBkJtM7x6PvYV6hmEm
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| Proof. cbv [pow_pred pow_N]; case Pos.pred_N; trivial. Qed. | ||
| End Pos. | ||
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| Module N. |
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This PR is clearly not ready. Additions to other types' namespaces should go in appropriate modules.
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Closing: the author of the development asked for this to go to mit-plv/fiat-crypto instead of stdlib for now. Sorry for the noise. |
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Adds
theories/ZArith/Factoring.v: the p-adic valuationval, the prime-power factorizationppfactor, the sorted prime factorizationfactorand Euler'stotienton positive numbers, all computable, with the fundamental theorem of arithmetic and the induction principlesfactor_indandppfactor_ind. The file comes from Andres Erbsen's WIP ZmodSqrt branch (andres-erbsen/stdlib@5bd6d0db), minus its unfinished scratch lemmas.Also adds the coprimality lemmas
Z.coprime_mul_l_iff,Z.coprime_mul_r_iff,Z.coprime_pow_l_iff,Z.coprime_pow_r_iffandZ.coprime_prime_primetoZdivisibility.v, and the generic list lemmas the file needs toList.v,Sorted.vandPermutation.v(Sorted.vnow requiresPermutation). A test file checks the computations.Written by Claude Fable 5.1.
🤖 Generated with Claude Code
https://claude.ai/code/session_01YJbiRBkJtM7x6PvYV6hmEm