Theorems · Theorem · number theory
Nat.mem_divisors
∀ {n m : ℕ}, n ∈ m.divisors ↔ n ∣ m ∧ m ≠ 0- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- zero_addproof · cited by 2,366
- eq_or_neproof · cited by 1,117
- Finset.Icoproof · cited by 450
- Finset.filter_congrproof · cited by 167
- Nat.divisorsstatement · cited by 137
- Ne.bot_ltproof · cited by 116
- Finset.Ico_eq_empty_of_leproof · cited by 22
- Finset.filter_trueproof · cited by 14
- Nat.filter_dvd_eq_divisorsproof · cited by 1
Cited by22
Results whose statement or proof uses this declaration.
- Nat.dvd_of_mem_divisorsproof · cited by 8
- Nat.pos_of_mem_divisorsproof · cited by 6
- Nat.mem_divisors_selfproof · cited by 6
- Nat.sum_div_divisorsproof · cited by 3
- Nat.sum_totientproof · cited by 3
- Nat.Prime.divisorsproof · cited by 3
- card_orderOf_eq_totient_aux₂proof · cited by 2
- card_addOrderOf_eq_totient_aux₂proof · cited by 2
- BoundingSieve.mainSum_lambdaSquared_eq_sum_sum_mulproof · cited by 1
- Nat.divisors_subset_of_dvdproof · cited by 1
- Nat.divisors_subset_properDivisorsproof · cited by 1
- Nat.mem_divisors_prime_powproof · cited by 1