Theorems · Theorem · number theory
PrimeMultiset.factorMultiset_prod
∀ (v : PrimeMultiset), v.prod.factorMultiset = v
If we start with a multiset of primes, take the product and then factor it, we get back the original multiset.
- Defined in
- Mathlib.Data.PNat.Factors
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetproof · cited by 2,627
- Nat.Primeproof · cited by 2,059
- Multiset.ofListproof · cited by 290
- Nat.primeFactorsListproof · cited by 105
- Nat.Primesproof · cited by 63
- PrimeMultisetstatement and proof · cited by 30
- PrimeMultiset.prodstatement and proof · cited by 23
- PNat.factorMultisetstatement and proof · cited by 18
- Multiset.coe_eq_coeproof · cited by 11
- PrimeMultiset.toNatMultisetproof · cited by 9
- Nat.primeFactorsList_uniqueproof · cited by 3
- PrimeMultiset.coe_prodproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- PNat.factorMultiset_le_iffproof · cited by 5
- PrimeMultiset.prod_dvd_iffproof · cited by 4
- PNat.factorMultiset_le_iff'proof · cited by 2
- PNat.factorMultisetEquivproof · cited by 1
- PNat.factorMultiset_mulproof · cited by 1
- PNat.factorMultiset_powproof · cited by 1
- PrimeMultiset.prod_supproof · cited by 0
- PrimeMultiset.prod_infproof · cited by 0