[Merged by Bors] - chore: deprecate prod_zero_iff_exists_zero
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Co-authored-by: Johan Commelin <johan@commelin.net>
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- Make `Multiset.prod_eq_zero_iff` a `simp` lemma. - Golf and deprecate `prod_zero_iff_exists_zero`; it was a bad API version of `Multiset.prod_eq_zero_iff`. - Make `Ideal.mul_eq_bot` a `simp` lemma`. - Add `Ideal.multiset_prod_eq_bot` (a `simp` lemma), deprecate `Ideal.prod_eq_bot`. The deprecated lemmas `prod_zero_iff_exists_zero` and `Ideal.prod_eq_bot` use `∃ x ∈ s, x = 0` instead of a simpler `0 ∈ s` in the RHS.
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prod_zero_iff_exists_zeroprod_zero_iff_exists_zero
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Multiset.prod_eq_zero_iffasimplemma.prod_zero_iff_exists_zero; it was a bad API version ofMultiset.prod_eq_zero_iff.Ideal.mul_eq_botasimplemma`.Ideal.multiset_prod_eq_bot(asimplemma), deprecateIdeal.prod_eq_bot.The deprecated lemmas
prod_zero_iff_exists_zeroandIdeal.prod_eq_botuse∃ x ∈ s, x = 0instead of a simpler0 ∈ sin the RHS.