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Theorems · Definition · number theory

PrimeMultiset

Type

The type of multisets of prime numbers. Unique factorization gives an equivalence between this set and ℕ+, as we will formalize below.

Defined in
Mathlib.Data.PNat.Factors
Cited by
30 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext
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Around this declaration

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

PrimeMultiset.prod · cited by 23PrimeMultiset.prodPNat.factorMultiset · cited by 18PNat.factorMultisetPrimeMultiset.toPNatMultiset · cited by 11PrimeMultiset.toPNatMulti…PrimeMultiset.toNatMultiset · cited by 9PrimeMultiset.toNatMultis…PrimeMultiset.factorMultiset_prod · cited by 7PrimeMultiset.factorMulti…PrimeMultiset.ofPrime · cited by 6PrimeMultiset.ofPrimePNat.factorMultiset_le_iff · cited by 5PNat.factorMultiset_le_iffPrimeMultiset.ofNatMultiset · cited by 5PrimeMultiset.ofNatMultis…PrimeMultiset.ofPNatMultiset · cited by 4PrimeMultiset.ofPNatMulti…PrimeMultiset.prod_dvd_iff · cited by 4PrimeMultiset.prod_dvd_iffPrimeMultiset.ofNatList · cited by 3PrimeMultiset.ofNatListPrimeMultiset.prod_add · cited by 3PrimeMultiset.prod_addPNat.factorMultiset_le_iff' · cited by 2PNat.factorMultiset_le_if…PrimeMultiset.coePNatMonoidHom · cited by 2PrimeMultiset.coePNatMono…PrimeMultiset.coe_prod · cited by 2PrimeMultiset.coe_prodMultiset · cited by 2627MultisetNat.Primes · cited by 63Nat.PrimesPrimeMultisetCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by42

Results whose statement or proof uses this declaration.