∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w : α),
  ¬[g a, g (g a)].Nodup →
    ∀ (w_1 : α),
      2 ≤ List.count w_1 [g a, g (g a)] →
        List.findIdxNth (fun x => decide (x = w)) [g (g a)] [g (g a)].length <
          (List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)]).length