∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w : α),
  2 ≤ List.count w [a, g a, g (g a)] →
    ¬[g a, g (g a)].Nodup →
      List.idxOfNth w [g (g a)] [g (g a)].length < (List.findIdxs (fun x => decide (x = w)) [a, g a, g (g a)]).length