let rec prf_of_prf_raw (prf_raw : t_prf_raw) : t_prf =
match prf_raw with
| Atomic_prf_raw fml_raw ->
Atomic_prf (fml_of_fml_raw fml_raw)
| Nullary_prf_raw (nullary_rule, fml_raw) ->
Nullary_prf (nullary_rule, fml_of_fml_raw fml_raw)
| Unary_prf_raw (prf_raw1, unary_rule, fml_raw) ->
Unary_prf (prf_of_prf_raw prf_raw1, unary_rule, fml_of_fml_raw fml_raw)
| Binary_prf_raw (prf_raw1, prf_raw2, binary_rule, fml_raw) ->
Binary_prf (prf_of_prf_raw prf_raw1, prf_of_prf_raw prf_raw2, binary_rule, fml_of_fml_raw fml_raw)
| Trinary_prf_raw (prf_raw1, prf_raw2, prf_raw3, trinary_rule, fml_raw) ->
Trinary_prf (prf_of_prf_raw prf_raw1, prf_of_prf_raw prf_raw2, prf_of_prf_raw prf_raw3, trinary_rule, fml_of_fml_raw fml_raw)