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Theorems · Theorem · commutative algebra

Associates.FactorSet.prod.eq_def

∀ {α : Type u_1} [inst : CommMonoidWithZero α] (x : Associates.FactorSet α),
  x.prod =
    match x with
    | none => 0
    | some s => (Multiset.map Subtype.val s).prod
Defined in
Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet
Cited by
2 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
CommMonoidWithZero
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Around this declaration

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

Associates.factors_prime_pow · cited by 2Associates.factors_prime_…Associates.factors_self · cited by 1Associates.factors_selfMultiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodIrreducible · cited by 496IrreducibleAssociates · cited by 210AssociatesAssociates.FactorSet · cited by 52Associates.FactorSetAssociates.FactorSet.prod · cited by 20FactorSet.prodprod.eq_defCITED BYCITES

Cites8

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Cited by2

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