Theorems · Theorem · group theory
Equiv.Perm.IsCycleOn.zpow_apply_eq
∀ {α : Type u_2} {f : Equiv.Perm α} {a : α} {s : Finset α},
f.IsCycleOn ↑s → a ∈ s → ∀ {n : ℤ}, (f ^ n) a = a ↔ ↑s.card ∣ n- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.cardstatement and proof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- inv_powproof · cited by 140
- zpow_negSuccproof · cited by 92
- Equiv.Perm.IsCycleOnstatement and proof · cited by 41
- dvd_negproof · cited by 19
- Equiv.Perm.IsCycleOn.pow_apply_eqproof · cited by 2
- Equiv.Perm.IsCycleOn.invproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycleOn.zpow_apply_eq_zpow_applyproof · cited by 1
- Equiv.Perm.IsCycleOn.pow_apply_eq_pow_applyproof · cited by 1