Theorems · Definition · group theory
Equiv.Perm.toList
{α : Type u_1} → [Fintype α] → [DecidableEq α] → Equiv.Perm α → α → List αEquiv.Perm.toList (f : Perm α) (x : α) generates the list [x, f x, f (f x), ...]
until looping. That means when f x = x, toList f x = [].
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Concrete
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Finset.cardproof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportproof · cited by 230
- Equiv.Perm.cycleOfproof · cited by 59
- List.iterateproof · cited by 15
Cited by25
Results whose statement or proof uses this declaration.
- Equiv.Perm.toCycleproof · cited by 7
- Equiv.Perm.length_toListstatement · cited by 6
- Equiv.Perm.nodup_toListstatement and proof · cited by 5
- Equiv.Perm.mem_toList_iffstatement · cited by 4
- Equiv.Perm.toCycle_eq_toListstatement and proof · cited by 4
- Equiv.Perm.toList_eq_nil_iffstatement · cited by 3
- Equiv.Perm.getElem_toListstatement and proof · cited by 3
- Equiv.Perm.toList_onestatement · cited by 2
- Equiv.Perm.next_toList_eq_applystatement and proof · cited by 2
- Equiv.Perm.exists_toCycle_toListstatement · cited by 2
- Equiv.Perm.toList_formPerm_isRotated_selfstatement and proof · cited by 1
- Equiv.Perm.toList_formPerm_nontrivialstatement · cited by 1