Theorems · Theorem · group theory
Equiv.Perm.toCycle_eq_toList
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (f : Equiv.Perm α) (hf : f.IsCycle) (x : α),
f x ≠ x → f.toCycle hf = ↑(f.toList x)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Concrete
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 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.
Cites17
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.univproof · cited by 3,473
- Multisetproof · cited by 2,627
- Equiv.Permstatement and proof · cited by 1,375
- Finset.valproof · cited by 438
- Multiset.consproof · cited by 313
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Multiset.eraseproof · cited by 93
- Cyclestatement and proof · cited by 79
- Cycle.ofListstatement and proof · cited by 38
- Cycle.nilproof · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.exists_toCycle_toListproof · cited by 2
- Equiv.Perm.nodup_toCycleproof · cited by 1
- Equiv.Perm.mem_toCycle_iff_supportproof · cited by 0
- Equiv.Perm.nontrivial_toCycleproof · cited by 0