∀ {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