Theorems · Theorem · group theory
Equiv.Perm.mem_toList_iff
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {p : Equiv.Perm α} {x y : α},
y ∈ p.toList x ↔ p.SameCycle x y ∧ x ∈ p.support- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Concrete
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.cardproof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.cycleOfproof · cited by 59
- Equiv.Perm.toListstatement · cited by 24
- Equiv.Perm.SameCycle.exists_pow_eq_of_mem_supportproof · cited by 5
- Equiv.Perm.support_cycleOf_eq_nil_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.next_toList_eq_applyproof · cited by 2
- Equiv.Perm.formPerm_toListproof · cited by 1
- Equiv.Perm.pow_apply_mem_toList_iff_mem_supportproof · cited by 0
- Equiv.Perm.mem_toCycle_iff_supportproof · cited by 0