Theorems · Theorem · group theory
Equiv.Perm.mem_support_iff_mem_support_of_mem_cycleFactorsFinset
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] {g : Equiv.Perm α} {x : α},
x ∈ g.support ↔ ∃ c ∈ g.cycleFactorsFinset, x ∈ c.support- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 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.
Cites10
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.cycleFactorsFinsetstatement and proof · cited by 96
- Equiv.Perm.cycleOfproof · cited by 59
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffproof · cited by 7
- Equiv.Perm.SameCycle.reflproof · cited by 7
- Equiv.Perm.mem_cycleFactorsFinset_support_leproof · cited by 7
- Equiv.Perm.mem_support_cycleOf_iffproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.