Theorems · Definition · group theory
Cycle.formPerm
{α : Type u_1} → [DecidableEq α] → (s : Cycle α) → s.Nodup → Equiv.Perm αA cycle s : Cycle α, given Nodup s can be interpreted as an Equiv.Perm α
where each element in the list is permuted to the next one, defined as formPerm.
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Concrete
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.Permstatement · cited by 1,375
- Cyclestatement and proof · cited by 79
- List.formPermproof · cited by 54
- List.IsRotatedproof · cited by 39
- Cycle.Nodupstatement and proof · cited by 28
- List.IsRotated.setoidproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.existsUnique_cyclestatement and proof · cited by 1
- Equiv.Perm.IsCycle.existsUnique_cycle_subtypestatement and proof · cited by 1
- Cycle.formPerm_subsingletonstatement · cited by 1
- Equiv.Perm.IsCycle.existsUnique_cycle_nontrivial_subtypestatement and proof · cited by 0
- Cycle.support_formPermstatement · cited by 0
- Cycle.formPerm_apply_mem_eq_nextstatement · cited by 0
- Cycle.formPerm_coestatement · cited by 0
- Cycle.formPerm_eq_formPerm_iffstatement and proof · cited by 0
- Cycle.formPerm_eq_self_of_notMemstatement · cited by 0
- Cycle.formPerm_reversestatement · cited by 0
- Cycle.isCycle_formPermstatement · cited by 0
- Equiv.Perm.isoCycleproof · cited by 0