Theorems · Theorem · group theory
Equiv.Perm.cycleOf_pow_apply_self
∀ {α : Type u_2} (f : Equiv.Perm α) [inst : DecidableRel f.SameCycle] (x : α) (n : ℕ), (f.cycleOf x ^ n) x = (f ^ n) x- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 5 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.
Cites7
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_succ'proof · cited by 228
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.cycleOfstatement and proof · cited by 59
- Equiv.Perm.mul_applyproof · cited by 38
- Equiv.Perm.cycleOf_applyproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.nodup_toListproof · cited by 5
- Equiv.Perm.cycleOf_zpow_apply_selfproof · cited by 2
- Equiv.Perm.pow_mod_card_support_cycleOf_self_applyproof · cited by 1
- Equiv.Perm.pow_mod_orderOf_cycleOf_applyproof · cited by 1
- Equiv.Perm.SameCycle.exists_pow_eqproof · cited by 0