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Theorems · Theorem · ring theory

TwoSidedIdeal.multiSetProd_mem

∀ {R : Type u_1} [inst : CommRing R] (I : TwoSidedIdeal R) {ι : Type u_2} (s : Multiset ι) (f : ι → R),
  (∃ x ∈ s, f x ∈ I) → (Multiset.map f s).prod ∈ I
Defined in
Mathlib.RingTheory.TwoSidedIdeal.BigOperators
Cited by
1 results in Mathlib
Foundations
Depth 43 from the axioms · uses propext, Quot.sound
Assumes
CommRing
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Around this declaration

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

TwoSidedIdeal.finsetProd_mem · cited by 2TwoSidedIdeal.finsetProd_…CommRing · cited by 17173CommRingMultiset · cited by 2627MultisetMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodTwoSidedIdeal · cited by 151TwoSidedIdealTwoSidedIdeal.listProd_mem · cited by 1TwoSidedIdeal.listProd_memTwoSidedIdeal.multiSetProd_memCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.