Theorems · Theorem · number theory
Nat.prod_mem_factoredNumbers
∀ (s : Finset ℕ) (n : ℕ), (List.filter (fun x => decide (x ∈ s)) n.primeFactorsList).prod ∈ Nat.factoredNumbers s
The product of the prime factors of n that are in s is an s-factored number.
- Defined in
- Mathlib.NumberTheory.SmoothNumbers
- Cited by
- 0 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.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Nat.Primeproof · cited by 2,059
- Nat.primeFactorsListstatement and proof · cited by 105
- LT.lt.falseproof · cited by 66
- Nat.factoredNumbersstatement · cited by 33
- Nat.prime_of_mem_primeFactorsListproof · cited by 30
- Nat.Prime.primeproof · cited by 19
- Nat.mem_primeFactorsListproof · cited by 9
- List.mem_of_mem_filterproof · cited by 4
- List.prod_ne_zeroproof · cited by 3
- Nat.pos_of_mem_primeFactorsListproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Nat.equivProdNatFactoredNumbersproof · cited by 4