feat: Add primeDivisors as an abbreviation for n.factorization.support
#7607
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FLDutchmann
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jcommelin
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Oct 12, 2023
FLDutchmann
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Oct 12, 2023
| #align nat.factor_iff_mem_factorization Nat.factor_iff_mem_factorization | ||
| #align nat.factor_iff_mem_factorization Nat.mem_primeDivisors_iff_factor | ||
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| theorem mem_primeDivisors {n p : ℕ} : p ∈ n.primeDivisors ↔ p.Prime ∧ p ∣ n ∧ n ≠ 0 := by |
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Sadly this can't be a simp lemma, because primeDivisors is an abbreviation and Finsupp.mem_support_iff gets to it first.
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Maybe you could instead add a simp lemma as n.factorization p ≠ 0 ↔ p.Prime ∧ p ∣ n ∧ n ≠ 0?
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This issue was solved by #8164 |
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Replace
n.factorization.supportandn.factors.toFinsetwithn.primeDivisorswherever possible. Also rename lemmas that usefactorizationto mean the Finset of prime divisors.see zulip
The biggest drawbacks with making it an abbreviation are that (1) we can't eliminate
factors.toFinsetlower down the import hierarchy, notably inNumberTheory/Divisors, and (2) we're missing out on an intuitivesimplemma that yieldsp.Prime ∧ p ∣ n ∧ n ≠ 0akin to Nat.mem_divisors. That said, people with much more experience than me have expressed a preference for this abbreviation, and indeed this change is relatively painless (modulo some renames).