Theorems · Theorem · group theory
Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iff
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {g : Equiv.Perm α} (a : g.Basis)
(τ : ↥(Equiv.Perm.OnCycleFactors.range_toPermHom' g)) {x : α} {c : ↥g.cycleFactorsFinset},
a.ofPermHomFun τ x ∈ (↑(↑τ c)).support ↔ x ∈ (↑c).support- Defined in
- Mathlib.GroupTheory.Perm.Centralizer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites25
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
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- Subtype.propproof · cited by 505
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.cycleFactorsFinsetstatement and proof · cited by 96
- Function.fixedPointsproof · cited by 90
- Equiv.Perm.Disjointproof · cited by 81
- Subtype.coe_ne_coeproof · cited by 27
- Equiv.Perm.Basisstatement and proof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.Basis.toCentralizer_equivariantproof · cited by 1