Theorems · Theorem · number theory
Nat.primeFactors_prod
∀ {s : Finset ℕ}, (∀ p ∈ s, Nat.Prime p) → (∏ p ∈ s, p).primeFactors = s- Defined in
- Mathlib.Data.Nat.Squarefree
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement and proof · cited by 2,356
- Nat.Primestatement and proof · cited by 2,059
- Finset.extproof · cited by 565
- Nat.primeFactorsstatement · cited by 129
- Nat.Prime.ne_zeroproof · cited by 109
- dvd_rflproof · cited by 80
- Nat.Prime.ne_oneproof · cited by 61
- Finset.prod_ne_zero_iffproof · cited by 45
- Nat.Prime.primeproof · cited by 19
- Prime.dvd_finsetProd_iffproof · cited by 7
- Nat.Prime.dvd_iff_eqproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Nat.primeFactors_prod_primeFactorsproof · cited by 2
- Nat.prod_primeFactors_invOn_squarefreeproof · cited by 1
- primeFactors_primorialproof · cited by 0