Theorems · Theorem · number theory
Nat.Prime.properDivisors
∀ {p : ℕ}, Nat.Prime p → p.properDivisors = {1}- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Nat.Primestatement and proof · cited by 2,059
- Finset.eraseproof · cited by 455
- Nat.Prime.ne_zeroproof · cited by 109
- Finset.mem_singletonproof · cited by 103
- Nat.Prime.ne_oneproof · cited by 61
- Nat.properDivisorsstatement · cited by 52
- Finset.erase_insertproof · cited by 21
- Nat.self_notMem_properDivisorsproof · cited by 14
- Finset.pair_commproof · cited by 5
- Nat.insert_self_properDivisorsproof · cited by 3
- Nat.Prime.divisorsproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Nat.Prime.prod_properDivisorsproof · cited by 1
- Nat.properDivisors_eq_singleton_one_iff_primeproof · cited by 1
- Nat.Prime.sum_properDivisorsproof · cited by 1
- Nat.Prime.not_pseudoperfectproof · cited by 1