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