Theorems · Theorem · group theory
Equiv.Perm.exists_toCycle_toList
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (f : Equiv.Perm α) (hf : f.IsCycle),
∃ x, f.toCycle hf = ↑(f.toList x)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Concrete
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCycleproof · cited by 116
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Cyclestatement · cited by 79
- Cycle.ofListstatement · cited by 38
- Equiv.Perm.toListstatement · cited by 24
- Equiv.Perm.toCyclestatement · cited by 7
- Equiv.Perm.toCycle_eq_toListproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.toCycle_nextproof · cited by 0
- Equiv.Perm.mem_toCycle_iff_supportproof · cited by 0