Theorems · Theorem · group theory
Equiv.Perm.two_le_card_support_cycleOf_iff
∀ {α : Type u_2} {f : Equiv.Perm α} {x : α} [inst : DecidableEq α] [inst_1 : Fintype α],
2 ≤ (f.cycleOf x).support.card ↔ f x ≠ x- 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.
Cites10
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
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.cycleOfstatement and proof · cited by 59
- Equiv.Perm.support_oneproof · cited by 10
- Equiv.Perm.isCycle_cycleOfproof · cited by 9
- Equiv.Perm.cycleOf_eq_one_iffproof · cited by 9
- Equiv.Perm.IsCycle.two_le_card_supportproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.support_cycleOf_nonemptyproof · cited by 0