Theorems · Theorem · group theory
Equiv.Perm.SameCycle.apply_eq_self_iff
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α}, f.SameCycle x y → (f x = x ↔ f y = y)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- add_commproof · cited by 1,535
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.injectiveproof · cited by 464
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.mul_applyproof · cited by 38
- zpow_add_oneproof · cited by 18
- zpow_one_addproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.isCycle_cycleOfproof · cited by 9
- Equiv.Perm.cycleOf_eq_one_iffproof · cited by 9
- Equiv.Perm.SameCycle.eq_of_rightproof · cited by 0