Theorems · Theorem · number theory
Nat.divisors_zero
Nat.divisors 0 = ∅
- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 64 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
- Finset.extproof · cited by 565
- Nat.divisorsstatement · cited by 137
Cited by12
Results whose statement or proof uses this declaration.
- Nat.sum_div_divisorsproof · cited by 3
- Nat.sum_totientproof · cited by 3
- ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eqproof · cited by 3
- ArithmeticFunction.vonMangoldt_sumproof · cited by 2
- IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRootsproof · cited by 2
- Nat.sum_divisors_eq_sum_properDivisors_add_selfproof · cited by 1
- Nat.nonempty_divisorsproof · cited by 1
- range_pow_padicValNat_subset_divisors'proof · cited by 1
- Nat.mul_divisors_filter_prime_powproof · cited by 1
- Nat.abundant_iff_two_lt_abundancyIndexproof · cited by 0
- Nat.prod_div_divisorsproof · cited by 0
- Nat.divisors_card_eq_one_iffproof · cited by 0