Theorems · Theorem · number theory
PNat.factorMultiset_ofPrime
∀ (p : Nat.Primes), (↑p).factorMultiset = PrimeMultiset.ofPrime p
Factoring a prime gives the corresponding one-element multiset.
- Defined in
- Mathlib.Data.PNat.Factors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.symmproof · cited by 3,681
- Equiv.injectiveproof · cited by 464
- PNatproof · cited by 392
- Nat.Primesstatement and proof · cited by 63
- PrimeMultisetstatement · cited by 30
- PrimeMultiset.prodproof · cited by 23
- PNat.factorMultisetstatement and proof · cited by 18
- Nat.Primes.toPNatstatement and proof · cited by 11
- PNat.prod_factorMultisetproof · cited by 9
- PrimeMultiset.ofPrimestatement and proof · cited by 6
- PNat.factorMultisetEquivproof · cited by 1
- PrimeMultiset.prod_ofPrimeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PNat.count_factorMultisetproof · cited by 0