Theorems · Theorem · group theory
finEquivPowers_symm_apply
∀ {G : Type u_1} [inst : Monoid G] {x : G} (hx : IsOfFinOrder x) (n : ℕ),
(finEquivPowers hx).symm ⟨x ^ n, ⋯⟩ = ⟨n % orderOf x, ⋯⟩- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- Monoidstatement and proof · cited by 3,887
- Equiv.symmstatement · cited by 3,681
- Submonoidstatement · cited by 3,086
- Submonoid.powersstatement and proof · cited by 408
- orderOfstatement and proof · cited by 324
- IsOfFinOrderstatement and proof · cited by 113
- Equiv.symm_apply_eqproof · cited by 63
- Subtype.mk_eq_mkproof · cited by 33
- IsOfFinOrder.orderOf_posstatement and proof · cited by 17
- pow_mod_orderOfproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- finEquivZPowers_symm_applyproof · cited by 1
- powersEquivPowers_applyproof · cited by 0