src/HOL/Tools/primrec_package.ML

     val _ = if gen_eq_set (op =) (names1, names2) then ()
       else primrec_error ("functions " ^ commas_quote names2 ^
         "\nare not mutually recursive");
     val qualify = NameSpace.qualified
       (space_implode "_" (map (Sign.base_name o #1) defs));
+    val spec' = (map o apfst o apfst) qualify spec;
     val simp_atts = map (Attrib.internal o K)
       [Simplifier.simp_add, RecfunCodegen.add NONE];
   in
     lthy
     |> set_group ? LocalTheory.set_group (serial_string ())
     |> fold_map (LocalTheory.define Thm.definitionK o make_def lthy fixes fs) defs
-    |-> (fn defs => `(fn ctxt => prove_spec ctxt names1 rec_rewrites defs spec))
+    |-> (fn defs => `(fn ctxt => prove_spec ctxt names1 rec_rewrites defs spec'))
     |-> (fn simps => fold_map (LocalTheory.note Thm.theoremK) simps)
     |-> (fn simps' => LocalTheory.note Thm.theoremK
           ((qualify "simps", simp_atts), maps snd simps'))
     |>> snd
   end handle PrimrecError (msg, some_eqn) =>