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Theorems · Theorem · ring theory

Multiset.prod_map_neg

∀ {M : Type u_2} [inst : CommMonoid M] [inst_1 : HasDistribNeg M] (s : Multiset M),
  (Multiset.map Neg.neg s).prod = (-1) ^ s.card * s.prod
Defined in
Mathlib.Algebra.BigOperators.Ring.Multiset
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
CommMonoidHasDistribNeg
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.prod_neg · cited by 2Finset.prod_negPolynomial.Splits.coeff_zero_eq_leadingCoeff_mul_prod_roots · cited by 1Splits.coeff_zero_eq_lead…Multiset · cited by 2627MultisetCommMonoid · cited by 2264CommMonoidMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodMultiset.card · cited by 375Multiset.cardHasDistribNeg · cited by 114HasDistribNegList.prod_map_neg · cited by 2List.prod_map_negMultiset.prod_map_negCITED BYCITES

Cites7

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Cited by2

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