Theorems · Theorem · group theory
Equiv.Perm.isSwap_iff_cycleType
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α}, σ.IsSwap ↔ σ.cycleType = {2}- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
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.
- Fintypestatement and proof · cited by 7,736
- Multisetstatement · cited by 2,627
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.sumproof · cited by 388
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- Equiv.Perm.IsSwapstatement and proof · cited by 35
- Multiset.sum_singletonproof · cited by 26
- Equiv.Perm.IsCycle.cycleTypeproof · cited by 12
- Equiv.Perm.IsSwap.isCycleproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleType_swap_mul_swap_of_nodupproof · cited by 1
- Equiv.Perm.IsSwap.orderOfproof · cited by 1