Theorems · Theorem · group theory
Equiv.Perm.cycleOf_eq_one_iff
∀ {α : Type u_2} {x : α} (f : Equiv.Perm α) [inst : DecidableRel f.SameCycle], f.cycleOf x = 1 ↔ f x = x- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 36 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.cycleOfstatement · cited by 59
- Equiv.Perm.SameCycle.reflproof · cited by 7
- Equiv.Perm.cycleOf_applyproof · cited by 6
- Equiv.Perm.SameCycle.apply_eq_self_iffproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffproof · cited by 7
- Equiv.Perm.cycleOf_oneproof · cited by 1
- Equiv.Perm.formPerm_toListproof · cited by 1
- Equiv.Perm.two_le_card_support_cycleOf_iffproof · cited by 1
- Equiv.Perm.eq_cycleOf_of_mem_cycleFactorsFinset_iffproof · cited by 1
- Equiv.Perm.cycleOf_ne_one_iff_mem_cycleFactorsFinsetproof · cited by 0
- Equiv.Perm.isCycle_cycleOf_iffproof · cited by 0
- Equiv.Perm.orderOf_cycleOf_dvd_orderOfproof · cited by 0
- Equiv.Perm.IsCycle.cycleOfproof · cited by 0