Theorems · Theorem · group theory
Equiv.Perm.isCycle_cycleOf
∀ {α : Type u_2} {x : α} (f : Equiv.Perm α) [inst : DecidableRel f.SameCycle], f x ≠ x → (f.cycleOf x).IsCycle- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 42 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.
Cites11
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.IsCyclestatement · cited by 108
- Equiv.Perm.cycleOfstatement and proof · cited by 59
- Equiv.Perm.cycleOf_apply_of_not_sameCycleproof · cited by 6
- Equiv.Perm.SameCycle.rflproof · cited by 5
- Equiv.Perm.SameCycle.cycleOf_applyproof · cited by 5
- Equiv.Perm.SameCycle.apply_eq_self_iffproof · cited by 3
- Equiv.Perm.isCycle_iff_sameCycleproof · cited by 3
- Equiv.Perm.cycleOf_zpow_apply_selfproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffproof · cited by 7
- Equiv.Perm.nodup_toListproof · cited by 5
- Equiv.Perm.next_toList_eq_applyproof · cited by 2
- Equiv.Perm.pow_mod_card_support_cycleOf_self_applyproof · cited by 1
- Equiv.Perm.two_le_card_support_cycleOf_iffproof · cited by 1
- Equiv.Perm.zpow_eq_zpow_on_iffproof · cited by 0
- Equiv.Perm.isCycle_cycleOf_iffproof · cited by 0
- Equiv.Perm.orderOf_cycleOf_dvd_orderOfproof · cited by 0
- Equiv.Perm.SameCycle.exists_pow_eqproof · cited by 0