∀ {α : Type u_1} {β : Type u_2} [inst : Primcodable α] [inst_1 : Primcodable β] {p : β → Prop}
  [inst_2 : DecidablePred p] {hp : PrimrecPred p} {f : α → Subtype p}, (Primrec fun a => ↑(f a)) ↔ Primrec f