Theorems · Theorem · group theory
Equiv.Perm.SameCycle.cycleOf_apply
∀ {α : Type u_2} {f : Equiv.Perm α} {x y : α} [inst : DecidableRel f.SameCycle], f.SameCycle x y → (f.cycleOf x) y = f y- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 35 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 · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.cycleOfstatement · cited by 59
- Equiv.Perm.subtypePermproof · cited by 35
- Equiv.Perm.ofSubtype_apply_of_memproof · cited by 11
- Equiv.Perm.sameCycle_apply_rightproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.isCycle_cycleOfproof · cited by 9
- Equiv.Perm.IsCycle.cycleOf_eqproof · cited by 5
- Equiv.Perm.cycleOf_apply_selfproof · cited by 5
- Equiv.Perm.SameCycle.cycleOf_eqproof · cited by 4
- Equiv.Perm.cycleOf_apply_apply_zpow_selfproof · cited by 2