Theorems · Theorem · group theory
Equiv.Perm.IsCycle.exists_pow_eq
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α} [Finite α], f.IsCycle → f x ≠ x → f y ≠ y → ∃ i, (f ^ i) x = y- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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.
- DFunLike.coestatement and proof · cited by 62,936
- Finitestatement and proof · cited by 3,029
- Equiv.Permstatement and proof · cited by 1,375
- ne_of_gtproof · cited by 637
- orderOfproof · cited by 324
- zpow_natCastproof · cited by 271
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- orderOf_posproof · cited by 15
- zpow_mod_orderOfproof · cited by 6
- Equiv.Perm.IsCycle.exists_zpow_eqproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Equiv.Perm.nodup_toListproof · cited by 5
- Equiv.Perm.IsCycle.support_pow_eq_iffproof · cited by 4
- Equiv.Perm.IsCycle.isConjproof · cited by 2
- Equiv.Perm.IsCycle.support_congrproof · cited by 1
- Equiv.Perm.IsCycle.eq_on_support_inter_nonempty_congrproof · cited by 1
- Equiv.Perm.closure_cycle_adjacent_swapproof · cited by 1
- Equiv.Perm.closure_prime_cycle_swapproof · cited by 1