Theorems · Theorem · group theory
sum_card_addOrderOf_eq_card_nsmul_eq_zero
∀ {G : Type u_1} [inst : AddMonoid G] {n : ℕ} [inst_1 : Fintype G] [inst_2 : DecidableEq G],
n ≠ 0 → ∑ m ∈ n.divisors, {x | addOrderOf x = m}.card = {x | n • x = 0}.card- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- AddMonoidstatement and proof · cited by 2,864
- Finset.cardstatement and proof · cited by 2,327
- Finset.filterstatement and proof · cited by 949
- Finset.extproof · cited by 565
- Finset.mem_univproof · cited by 361
- SetLike.mem_coeproof · cited by 302
- Finset.biUnionproof · cited by 217
- addOrderOfstatement and proof · cited by 208
Cited by1
Results whose statement or proof uses this declaration.
- card_addOrderOf_eq_totient_aux₂proof · cited by 2