Theorems · Theorem · number theory
Nat.properDivisors_zero
Nat.properDivisors 0 = ∅
- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 6 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.properDivisorsstatement · cited by 52
Cited by6
Results whose statement or proof uses this declaration.
- Nat.eq_properDivisors_of_subset_of_sum_eq_sumproof · cited by 2
- Nat.sum_properDivisors_eq_one_iff_primeproof · cited by 1
- Nat.sum_divisors_eq_sum_properDivisors_add_selfproof · cited by 1
- Nat.abundant_iff_two_lt_abundancyIndexproof · cited by 0
- Nat.coe_properDivisors_eq_prod_pow_lt_factorizationproof · cited by 0
- Nat.sum_properDivisors_dvdproof · cited by 0