Mathlib Map

Theorems · Theorem · group theory

Equiv.Perm.cycleOf_self_apply_pow

∀ {α : Type u_2} (f : Equiv.Perm α) [inst : DecidableRel f.SameCycle] (n : ℕ) (x : α),
  f.cycleOf ((f ^ n) x) = f.cycleOf x
Defined in
Mathlib.GroupTheory.Perm.Cycle.Factors
Cited by
1 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableRel
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Equiv.Perm.toList_pow_apply_eq_rotate · cited by 1Perm.toList_pow_apply_eq_…DFunLike.coe · cited by 62936DFunLike.coeEquiv.Perm · cited by 1375Equiv.PermEquiv.Perm.SameCycle · cited by 116Perm.SameCycleEquiv.Perm.cycleOf · cited by 59Perm.cycleOfEquiv.Perm.SameCycle.rfl · cited by 5SameCycle.rflEquiv.Perm.SameCycle.cycleOf_eq · cited by 4SameCycle.cycleOf_eqEquiv.Perm.SameCycle.pow_left · cited by 1SameCycle.pow_leftPerm.cycleOf_self_apply_powCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.