Theorems · Theorem · group theory
Equiv.Perm.IsCycle.zpowersEquivSupport_apply
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] {σ : Equiv.Perm α} (hσ : σ.IsCycle) {n : ℕ},
hσ.zpowersEquivSupport ⟨σ ^ n, ⋯⟩ = ⟨(σ ^ n) (Classical.choose hσ), ⋯⟩- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement · cited by 13,712
- Equivstatement · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
- Subgroup.zpowersstatement · cited by 204
- Equiv.Perm.SameCyclestatement · cited by 116
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Equiv.Perm.mem_supportstatement · cited by 51
- Equiv.Perm.IsCycle.zpowersEquivSupportstatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.zpowersEquivSupport_symm_applyproof · cited by 1