Theorems · Definition · group theory
Equiv.Perm.SameCycle
{α : Type u_2} → Equiv.Perm α → α → α → PropThe equivalence relation indicating that two points are in the same cycle of a permutation.
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 116 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 198 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
Cited by120
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycleproof · cited by 108
- Equiv.Perm.cycleOfstatement and proof · cited by 59
- Equiv.Perm.IsCycleOnproof · cited by 41
- Equiv.Perm.IsCycle.ne_oneproof · cited by 11
- Equiv.Perm.cycleOf_eq_one_iffstatement and proof · cited by 9
- Equiv.Perm.isCycle_cycleOfstatement and proof · cited by 9
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffproof · cited by 7
- Equiv.Perm.SameCycle.reflstatement · cited by 7
- Equiv.Perm.SameCycle.symmstatement and proof · cited by 7
- Equiv.Perm.sameCycle_apply_rightstatement and proof · cited by 7
- Equiv.Perm.cycleOf_applystatement and proof · cited by 6
- Equiv.Perm.cycleOf_apply_of_not_sameCyclestatement and proof · cited by 6