Theorems · Theorem · number theory
Nat.prod_primeFactors_sdiff_of_squarefree
∀ {n : ℕ}, Squarefree n → ∀ {t : Finset ℕ}, t ⊆ n.primeFactors → ∏ a ∈ n.primeFactors \ t, a = n / ∏ a ∈ t, a- Defined in
- Mathlib.Data.Nat.Squarefree
- 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.
Cites11
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 · cited by 2,356
- Nat.primeFactorsstatement and proof · cited by 129
- Squarefreestatement and proof · cited by 112
- Nat.Prime.posproof · cited by 83
- symmproof · cited by 48
- Nat.prime_of_mem_primeFactorsListproof · cited by 30
- Finset.prod_posproof · cited by 25
- List.mem_toFinsetproof · cited by 20
- Finset.prod_sdiffproof · cited by 10
- Nat.prod_primeFactors_of_squarefreeproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefreeproof · cited by 1