Theorems · Theorem · group theory
Equiv.Perm.SameCycle.mem_support_iff
∀ {α : Type u_2} {x y : α} {f : Equiv.Perm α} [inst : DecidableEq α] [inst_1 : Fintype α],
f.SameCycle x y → (x ∈ f.support ↔ y ∈ f.support)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.SameCyclestatement and proof · cited by 116
- Equiv.Perm.SameCycle.symmproof · cited by 7
- Equiv.Perm.mem_support_cycleOf_iffproof · cited by 4
- Equiv.Perm.support_cycleOf_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.SameCycle.toList_isRotatedproof · cited by 0