Theorems · Theorem · group theory
Equiv.Perm.zpow_apply_eq_self_of_apply_eq_self
∀ {α : Type u_1} {f : Equiv.Perm α} {x : α}, f x = x → ∀ (n : ℤ), (f ^ n) x = x- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Equiv.Permstatement and proof · cited by 1,375
- zpow_negSuccproof · cited by 92
- Equiv.Perm.inv_eq_iff_eqproof · cited by 8
- Equiv.Perm.pow_apply_eq_self_of_apply_eq_selfproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Equiv.Perm.support_zpow_leproof · cited by 4
- Equiv.Perm.Disjoint.zpow_disjoint_zpowproof · cited by 3
- Equiv.Perm.isCycle_iff_sameCycleproof · cited by 3
- Equiv.Perm.cycleOf_mul_of_apply_right_eq_selfproof · cited by 2
- Equiv.Perm.set_support_zpow_subsetproof · cited by 2
- Equiv.Perm.SameCycle.exists_pow_eqproof · cited by 0