store the {l,g}fp-definition and the monotonicity theorem for inductive predicates (by Jan van Brügge)

--- a/src/HOL/Tools/inductive.ML	Wed Jan 15 13:54:28 2025 +0100
+++ b/src/HOL/Tools/inductive.ML	Wed Jan 15 13:55:58 2025 +0100
@@ -21,7 +21,7 @@
 signature INDUCTIVE =
 sig
   type result =
-    {preds: term list, elims: thm list, raw_induct: thm,
+    {preds: term list, elims: thm list, raw_induct: thm, def: thm, mono: thm,
      induct: thm, inducts: thm list, intrs: thm list, eqs: thm list}
   val transform_result: morphism -> result -> result
   type info = {names: string list, coind: bool} * result
@@ -180,17 +180,18 @@
 (** context data **)
 
 type result =
-  {preds: term list, elims: thm list, raw_induct: thm,
+  {preds: term list, elims: thm list, raw_induct: thm, def: thm, mono: thm,
    induct: thm, inducts: thm list, intrs: thm list, eqs: thm list};
 
-fun transform_result phi {preds, elims, raw_induct: thm, induct, inducts, intrs, eqs} =
+fun transform_result phi {preds, elims, raw_induct: thm, induct, inducts, intrs, eqs, def, mono} =
   let
     val term = Morphism.term phi;
     val thm = Morphism.thm phi;
     val fact = Morphism.fact phi;
   in
-   {preds = map term preds, elims = fact elims, raw_induct = thm raw_induct,
-    induct = thm induct, inducts = fact inducts, intrs = fact intrs, eqs = fact eqs}
+   {preds = map term preds, elims = fact elims, raw_induct = thm raw_induct, def = thm def,
+    induct = thm induct, inducts = fact inducts, intrs = fact intrs, eqs = fact eqs,
+    mono = thm mono}
   end;
 
 type info = {names: string list, coind: bool} * result;
@@ -1152,6 +1153,8 @@
        raw_induct = rulify lthy3 raw_induct,
        induct = induct,
        inducts = inducts,
+       def = fp_def,
+       mono = mono,
        eqs = eqs'};
 
     val lthy4 = lthy3

--- a/src/HOL/Tools/inductive_set.ML	Wed Jan 15 13:54:28 2025 +0100
+++ b/src/HOL/Tools/inductive_set.ML	Wed Jan 15 13:55:58 2025 +0100
@@ -463,7 +463,7 @@
         eta_contract (member op = cs' orf is_pred pred_arities))) intros;
     val cnames_syn' = map (fn (b, _) => (Binding.suffix_name "p" b, NoSyn)) cnames_syn;
     val monos' = map (to_pred [] (Context.Proof lthy)) monos;
-    val ({preds, intrs, elims, raw_induct, eqs, ...}, lthy1) =
+    val ({preds, intrs, elims, raw_induct, eqs, def, mono, ...}, lthy1) =
       Inductive.add_ind_def
         {quiet_mode = quiet_mode, verbose = verbose, alt_name = Binding.empty,
           coind = coind, no_elim = no_elim, no_ind = no_ind, skip_mono = skip_mono}
@@ -513,7 +513,7 @@
         (map (to_set [] (Context.Proof lthy3)) eqs) raw_induct' lthy3;
   in
     ({intrs = intrs', elims = elims', induct = induct, inducts = inducts,
-      raw_induct = raw_induct', preds = map fst defs, eqs = eqs'},
+      raw_induct = raw_induct', preds = map fst defs, eqs = eqs', def = def, mono = mono},
      lthy4)
   end;