Theorems · Theorem · group theory
Equiv.Perm.IsCycleOn.apply_ne
∀ {α : Type u_2} {f : Equiv.Perm α} {s : Set α} {a : α}, f.IsCycleOn s → s.Nontrivial → a ∈ s → f a ≠ a- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Setstatement and proof · cited by 53,352
- Equiv.Permstatement and proof · cited by 1,375
- Set.Nontrivialstatement and proof · cited by 145
- Equiv.Perm.IsCycleOnstatement and proof · cited by 41
- Set.Nontrivial.exists_neproof · cited by 8
- Function.IsFixedPt.perm_zpowproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycleOn.pow_apply_eqproof · cited by 2
- Equiv.Perm.IsCycleOn.isCycle_subtypePermproof · cited by 2
- Equiv.Perm.IsCycleOn.subtypePermproof · cited by 0
- Equiv.Perm.isCycle_iff_exists_isCycleOnproof · cited by 0