Theorems · Definition · group theory
Equiv.Perm.cycleOf
{α : Type u_2} → (f : Equiv.Perm α) → [DecidableRel f.SameCycle] → α → Equiv.Perm αf.cycleOf x is the cycle of the permutation f to which x belongs.
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableRel
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.
- DFunLike.coeproof · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.ofSubtypeproof · cited by 41
- Equiv.Perm.subtypePermproof · cited by 35
- Equiv.Perm.sameCycle_apply_rightproof · cited by 7
Cited by62
Results whose statement or proof uses this declaration.
- Equiv.Perm.toListproof · cited by 24
- Equiv.Perm.isCycle_cycleOfstatement and proof · cited by 9
- Equiv.Perm.cycleOf_eq_one_iffstatement · cited by 9
- Equiv.Perm.Basis.ofPermHomFunproof · cited by 9
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffstatement and proof · cited by 7
- Equiv.Perm.length_toListstatement and proof · cited by 6
- Equiv.Perm.cycleOf_applystatement · cited by 6
- Equiv.Perm.cycleOf_apply_of_not_sameCyclestatement · cited by 6
- Equiv.Perm.SameCycle.cycleOf_applystatement · cited by 5
- Equiv.Perm.SameCycle.exists_pow_eq_of_mem_supportstatement · cited by 5
- Equiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eqproof · cited by 5
- Equiv.Perm.nodup_toListproof · cited by 5