Theorems · Theorem · group theory
zpow_eq_zpow_iff_modEq
∀ {G : Type u_1} [inst : Group G] {x : G} {m n : ℤ}, x ^ m = x ^ n ↔ m ≡ n [ZMOD ↑(orderOf x)]- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- zero_subproof · cited by 335
- orderOfstatement and proof · cited by 324
- neg_subproof · cited by 272
- Int.ModEqstatement and proof · cited by 147
- mul_inv_eq_oneproof · cited by 20
- Int.modEq_iff_dvdproof · cited by 16
- zpow_subproof · cited by 15
- zpow_eq_one_iff_modEqproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- monoidHomOfForallMemZpowers_apply_genproof · cited by 4
- injective_zpow_iff_not_isOfFinOrderproof · cited by 1
- MulDistribMulAction.toMonoidHomZModOfIsCyclic_applyproof · cited by 1
- IsPGroup.smul_mul_inv_trivial_or_surjectiveproof · cited by 1
- IsCyclic.unique_zpow_zmodproof · cited by 0