Theorems · Theorem · group theory
Equiv.Perm.SameCycle.symm
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α}, f.SameCycle x y → f.SameCycle y x- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 7 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.
Cites5
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
- Equiv.symm_apply_applyproof · cited by 320
- zpow_negproof · cited by 198
- Equiv.Perm.SameCyclestatement and proof · cited by 116
Cited by7
Results whose statement or proof uses this declaration.
- Equiv.Perm.SameCycle.cycleOf_eqproof · cited by 4
- Equiv.Perm.sameCycle_commproof · cited by 2
- Equiv.Perm.Basis.sameCycleproof · cited by 2
- Equiv.Perm.SameCycle.mem_support_iffproof · cited by 1
- Equiv.Perm.pow_apply_mem_toList_iff_mem_supportproof · cited by 0
- Equiv.Perm.SameCycle.equivalenceproof · cited by 0
- Equiv.Perm.cycleOf_self_applyproof · cited by 0