Theorems · Theorem · number theory
Nat.dvd_of_mem_divisors
∀ {n m : ℕ}, n ∈ m.divisors → n ∣ m- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Nat.divisorsstatement and proof · cited by 137
- Nat.mem_divisorsproof · cited by 22
Cited by8
Results whose statement or proof uses this declaration.
- Nat.sum_totientproof · cited by 3
- ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq_onproof · cited by 3
- tsum_prod_pow_eq_tsum_sigmaproof · cited by 2
- BoundingSieve.mainSum_lambdaSquared_eq_sum_sum_mulproof · cited by 1
- Nat.divisors_filter_squarefree_of_squarefreeproof · cited by 1
- BoundingSieve.upperMoebius_lambdaSquaredproof · cited by 0
- Nat.coe_divisors_eq_prod_pow_le_factorizationproof · cited by 0
- BoundingSieve.mainSum_lambdaSquared_eq_sum_mul_sum_sqproof · cited by 0