Theorems · Theorem · group theory
Equiv.Perm.SameCycle.cycleOf_eq
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α} [inst : DecidableRel f.SameCycle],
f.SameCycle x y → f.cycleOf x = f.cycleOf y- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableRel
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.coeproof · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.extproof · cited by 75
- Equiv.Perm.cycleOfstatement and proof · cited by 59
- Equiv.Perm.SameCycle.symmproof · cited by 7
- Equiv.Perm.cycleOf_applyproof · cited by 6
- Equiv.Perm.cycleOf_apply_of_not_sameCycleproof · cited by 6
- Equiv.Perm.SameCycle.cycleOf_applyproof · cited by 5
- Equiv.Perm.SameCycle.transproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleOf_self_apply_zpowproof · cited by 1
- Equiv.Perm.cycleOf_self_apply_powproof · cited by 1
- Equiv.Perm.sameCycle_iff_cycleOf_eq_of_mem_supportproof · cited by 0
- Equiv.Perm.cycleOf_self_applyproof · cited by 0