Theorems · Theorem · group theory
Equiv.Perm.IsCycle.cycleOf_eq
∀ {α : Type u_2} {f : Equiv.Perm α} {x : α} [inst : DecidableRel f.SameCycle], f.IsCycle → f x ≠ x → f.cycleOf x = f- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 5 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.
Cites9
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 and proof · cited by 108
- Equiv.extproof · cited by 102
- Equiv.Perm.cycleOfstatement · cited by 59
- Equiv.Perm.cycleOf_apply_of_not_sameCycleproof · cited by 6
- Equiv.Perm.SameCycle.cycleOf_applyproof · cited by 5
- Equiv.Perm.isCycle_iff_sameCycleproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycle_is_cycleOfproof · cited by 4
- Equiv.Perm.IsCycle.existsUnique_cycleproof · cited by 1
- Equiv.Perm.toList_formPerm_nontrivialproof · cited by 1
- Equiv.Perm.IsCycle.cycleOfproof · cited by 0
- List.cycleOf_formPermproof · cited by 0