Theorems · Theorem · group theory
zpow_pow_orderOf
∀ {G : Type u_1} [inst : Group G] {x : G} {i : ℤ}, (x ^ i) ^ orderOf x = 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 37 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.
Cites10
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
- mul_commproof · cited by 2,262
- pow_zeroproof · cited by 1,094
- orderOfstatement and proof · cited by 324
- zpow_natCastproof · cited by 271
- IsOfFinOrderproof · cited by 113
- one_zpowproof · cited by 44
- pow_orderOf_eq_oneproof · cited by 30
- zpow_mulproof · cited by 27
- orderOf_eq_zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsOfFinOrder.zpowproof · cited by 1
- orderOf_dvd_of_mem_zpowersproof · cited by 0