Theorems · Theorem · group theory
Equiv.Perm.IsCycleOn.apply_mem_iff
∀ {α : Type u_2} {f : Equiv.Perm α} {s : Set α} {x : α}, f.IsCycleOn s → (f x ∈ s ↔ x ∈ s)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 3 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
- Equiv.symm_apply_applyproof · cited by 320
- Set.BijOn.mapsToproof · cited by 42
- Equiv.Perm.IsCycleOnstatement and proof · cited by 41
- Set.BijOn.perm_invproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycleOn.pow_apply_eqproof · cited by 2
- Equiv.Perm.IsCycleOn.isCycle_subtypePermstatement and proof · cited by 2
- Equiv.Perm.IsCycleOn.subtypePermstatement and proof · cited by 0