∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w w_1 : α),
  List.findIdxNth (fun x => decide (x = w_1)) [g a, g (g a)] (List.idxOfNth w [g (g a)] 1) + 1 ≤
      (List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)]).length →
    List.findIdxNth (fun x => decide (x = w_1)) [g a, g (g a)] (List.idxOfNth w [g (g a)] 1) <
      (List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)]).length