∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w : α) (h_2 : 2 ≤ List.count w [a, g a, g (g a)])
  (h_3 : ¬[g a, g (g a)].Nodup) (w_1 : α) (h_5 : 2 ≤ List.count w_1 [g a, g (g a)]),
  (List.findIdxs (fun x => decide (x = w_1))
        [g a,
          g (g a)])[(List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)])[List.idxOfNth w_1 [g a, g (g a)] 1]] <
    [g a, g (g a)].length