∀ {motive_1 : Aesop.Script.StepTree → Sort u} {motive_2 : Array Aesop.Script.StepTree → Sort u}
  {motive_3 : List Aesop.Script.StepTree → Sort u} (t : Array Aesop.Script.StepTree)
  (F_1 : (t : Aesop.Script.StepTree) → t.below → motive_1 t)
  (F_2 : (t : Array Aesop.Script.StepTree) → Aesop.Script.StepTree.below_1 t → motive_2 t)
  (F_3 : (t : List Aesop.Script.StepTree) → Aesop.Script.StepTree.below_2 t → motive_3 t),
  Aesop.Script.StepTree.brecOn_1 t F_1 F_2 F_3 = F_2 t (Aesop.Script.StepTree.brecOn_1.go t F_1 F_2 F_3).2