Theorems · Theorem · number theory
Nat.mem_properDivisors
∀ {n m : ℕ}, n ∈ m.properDivisors ↔ n ∣ m ∧ n < m- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 15 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- eq_or_neproof · cited by 1,117
- Finset.Icoproof · cited by 450
- Finset.filter_congrproof · cited by 167
- Nat.properDivisorsstatement · cited by 52
- Finset.Ico_eq_empty_of_leproof · cited by 22
- Finset.filter_trueproof · cited by 14
- Nat.filter_dvd_eq_properDivisorsproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_eq_prod_X_sub_primitiveRootsproof · cited by 5
- Nat.one_mem_properDivisors_iff_one_ltproof · cited by 4
- Polynomial.cyclotomic_coeff_zeroproof · cited by 3
- Polynomial.int_coeff_of_cyclotomic'proof · cited by 3
- Nat.mem_properDivisors_prime_powproof · cited by 1
- Nat.divisors_subset_properDivisorsproof · cited by 1
- Polynomial.cyclotomic_posproof · cited by 1
- Nat.properDivisors_eq_singleton_one_iff_primeproof · cited by 1
- Nat.one_lt_div_of_mem_properDivisorsproof · cited by 1
- Nat.one_lt_of_mem_properDivisorsproof · cited by 1
- Nat.mem_properDivisors_iff_existsproof · cited by 0
- Polynomial.X_pow_sub_one_mul_cyclotomic_dvd_X_pow_sub_one_of_dvdproof · cited by 0