Theorems · Theorem · group theory
Equiv.Perm.support_cycleOf_eq_nil_iff
∀ {α : Type u_2} {f : Equiv.Perm α} {x : α} [inst : DecidableEq α] [inst_1 : Fintype α],
(f.cycleOf x).support = ∅ ↔ x ∉ f.support- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
- Equiv.Perm.cycleOfstatement · cited by 59
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.mem_toList_iffproof · cited by 4