∀ {α' : Type u_9} {β' : Type u_10} (e e_1 : Equiv.Perm α'),
  e = e_1 →
    ∀ {p : β' → Prop} {inst : DecidablePred p} [inst_1 : DecidablePred p] (f f_1 : α' ≃ Subtype p),
      f = f_1 → e.extendDomain f = e_1.extendDomain f_1