Theorems · Theorem · group theory
IsCyclic.card_pow_eq_one_le
∀ {α : Type u_1} [inst : Group α] [inst_1 : DecidableEq α] [inst_2 : Fintype α] [IsCyclic α] {n : ℕ},
0 < n → {a | a ^ n = 1}.card ≤ n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Groupstatement and proof · cited by 6,238
- Finset.univstatement and proof · cited by 3,473
- Finset.cardstatement and proof · cited by 2,327
- MulZeroClass.mul_zeroproof · cited by 2,091
- Fintype.cardproof · cited by 1,386
- Finset.filterstatement and proof · cited by 949
- Submonoid.powersproof · cited by 408
- orderOfproof · cited by 324
- zpow_natCastproof · cited by 271
- Set.toFinsetproof · cited by 217
Cited by2
Results whose statement or proof uses this declaration.
- FiniteField.unitsMap_norm_surjectiveproof · cited by 1
- IsCyclic.card_orderOf_eq_totientproof · cited by 0