Theorems · Theorem · ring theory
List.prod_map_neg
∀ {M : Type u_3} [inst : Monoid M] [inst_1 : HasDistribNeg M] (l : List M),
(List.map Neg.neg l).prod = (-1) ^ l.length * l.prod- Defined in
- Mathlib.Algebra.BigOperators.Ring.List
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- MonoidHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- pow_zeroproof · cited by 1,094
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- pow_succproof · cited by 374
- HasDistribNegstatement and proof · cited by 114
- Commute.pow_leftproof · cited by 9
- Commute.left_commproof · cited by 9
- Commute.neg_one_leftproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.ofScalars_comp_neg_idproof · cited by 3
- Multiset.prod_map_negproof · cited by 2