Theorems · Theorem · group theory
Equiv.Perm.IsCycle.cycleType
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α},
σ.IsCycle → σ.cycleType = {σ.support.card}- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 97 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.
Cites10
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
- mul_oneproof · cited by 3,885
- Multisetstatement · cited by 2,627
- Finset.cardstatement · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Equiv.Perm.cycleTypestatement · cited by 87
- Equiv.Perm.Disjointproof · cited by 81
- Equiv.Perm.cycleType_eqproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- Equiv.Perm.sum_cycleTypeproof · cited by 14
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Equiv.Perm.cycleType_extendDomainproof · cited by 3
- Equiv.Perm.sign_of_cycleType'proof · cited by 2
- cycleType_finRotateproof · cited by 2
- Equiv.Perm.cycleType_conjproof · cited by 2
- Equiv.Perm.mem_cycleType_iffproof · cited by 2
- Equiv.Perm.isSwap_iff_cycleTypeproof · cited by 2
- Equiv.Perm.isConj_of_cycleType_eqproof · cited by 1
- Equiv.Perm.cycleType_invproof · cited by 1
- alternatingGroup.isConj_swap_mul_swap_of_cycleType_twoproof · cited by 0
- Equiv.Perm.cycleType_of_card_le_mem_cycleType_add_twoproof · cited by 0