Theorems · Theorem · group theory
Equiv.Perm.sameCycle_apply_right
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α}, f.SameCycle x (f y) ↔ f.SameCycle x y- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 33 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.coestatement · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.sameCycle_apply_leftproof · cited by 4
- Equiv.Perm.sameCycle_commproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleOfproof · cited by 59
- Equiv.Perm.cycleOf_apply_of_not_sameCycleproof · cited by 6
- Equiv.Perm.cycleOf_applyproof · cited by 6
- Equiv.Perm.SameCycle.cycleOf_applyproof · cited by 5
- Equiv.Perm.sameCycle_symm_apply_rightproof · cited by 2
- Equiv.Perm.cycleOf_self_applyproof · cited by 0
- Equiv.Perm.SameCycle.apply_rightproof · cited by 0
- Equiv.Perm.SameCycle.of_apply_rightproof · cited by 0