Theorems · Theorem · group theory
Equiv.Perm.sameCycle_apply_left
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α}, f.SameCycle (f x) y ↔ f.SameCycle x y- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 4 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.
Cites10
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
- Equiv.Permstatement and proof · cited by 1,375
- pow_oneproof · cited by 894
- Equiv.symm_apply_applyproof · cited by 320
- zpow_ofNatproof · cited by 144
- Equiv.Perm.SameCyclestatement · cited by 116
- Equiv.exists_congr_leftproof · cited by 33
- Equiv.addRightproof · cited by 30
- zpow_subproof · cited by 15
- Equiv.addRight_symmproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.sameCycle_apply_rightproof · cited by 7
- Equiv.Perm.sameCycle_symm_apply_leftproof · cited by 2
- Equiv.Perm.SameCycle.of_apply_leftproof · cited by 0
- Equiv.Perm.SameCycle.apply_leftproof · cited by 0