∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w : α)
  (h :
    List.idxOfNth w [g (g a)] {g a, g (g a)}.card + 1 ≤
      (List.filter (fun x => decide (x = w)) [a, g a, g (g a)]).length),
  (List.findIdxs (fun x => decide (x = w)) [a, g a, g (g a)])[List.idxOfNth w [g (g a)] {g a, g (g a)}.card] <
    [a, g a, g (g a)].length