Theorems · Theorem · group theory
Equiv.Perm.IsCycle.of_pow
∀ {α : Type u_2} {f : Equiv.Perm α} [inst : DecidableEq α] [inst_1 : Fintype α] {n : ℕ},
(f ^ n).IsCycle → f.support ⊆ (f ^ n).support → f.IsCycle- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
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.coeproof · cited by 62,936
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- LE.le.antisymmproof · cited by 507
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.SameCycleproof · cited by 116
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- zpow_mulproof · cited by 27
- Equiv.Perm.support_pow_leproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.pow_iffproof · cited by 1
- Equiv.Perm.closure_cycle_coprime_swapproof · cited by 1
- Equiv.Perm.IsCycle.of_zpowproof · cited by 0