Theorems · Theorem · number theory
Nat.eq_properDivisors_of_subset_of_sum_eq_sum
∀ {n : ℕ} {s : Finset ℕ}, s ⊆ n.properDivisors → ∑ x ∈ s, x = ∑ x ∈ n.properDivisors, x → s = n.properDivisors- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Finset.sumstatement and proof · cited by 5,195
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- Finset.Nonemptyproof · cited by 1,001
- add_assocproof · cited by 746
- Finset.sum_const_zeroproof · cited by 219
- Nat.properDivisorsstatement and proof · cited by 52
- add_lt_add_leftproof · cited by 47
- Finset.sdiff_subsetproof · cited by 21
- Finset.sum_sdiffproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Nat.sum_properDivisors_eq_one_iff_primeproof · cited by 1
- Nat.sum_properDivisors_dvdproof · cited by 0