Theorems · Theorem · group theory
Equiv.Perm.eq_cycleOf_of_mem_cycleFactorsFinset_iff
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] (g c : Equiv.Perm α),
c ∈ g.cycleFactorsFinset → ∀ (x : α), c = g.cycleOf x ↔ x ∈ c.support- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 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.
Cites13
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 and proof · cited by 230
- Equiv.Perm.cycleFactorsFinsetstatement and proof · cited by 96
- Equiv.Perm.cycleOfstatement and proof · cited by 59
- Equiv.Perm.mem_supportproof · cited by 51
- Equiv.Perm.mem_cycleFactorsFinset_iffproof · cited by 17
- Equiv.Perm.IsCycle.ne_oneproof · cited by 11
- Equiv.Perm.cycleOf_eq_one_iffproof · cited by 9
- Equiv.Perm.cycleOf_apply_selfproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.zpow_apply_mem_support_of_mem_cycleFactorsFinset_iffproof · cited by 3