Theorems · Theorem · group theory
Equiv.Perm.IsCycle.exists_zpow_eq
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α}, f.IsCycle → f x ≠ x → f y ≠ y → ∃ i, (f ^ i) x = y- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.IsCyclestatement · cited by 108
- Equiv.Perm.IsCycle.sameCycleproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.exists_pow_eqproof · cited by 7
- Equiv.Perm.isCycle_iff_sameCycleproof · cited by 3
- Equiv.Perm.IsCycle.swap_mulproof · cited by 0