∀ {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)]),
  (List.findIdxs (fun x => decide (x = w)) [a, g a, g (g a)])[List.idxOfNth w [] [].length] < [a, g a, g (g a)].length