careful with op = in n2m (actually by Dmitriy Traytel)

--- a/src/HOL/Tools/BNF/bnf_fp_n2m.ML	Thu Sep 18 16:47:40 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_fp_n2m.ML	Thu Sep 18 16:47:40 2014 +0200
@@ -182,12 +182,13 @@
     val castAs = map2 (curry HOLogic.mk_comp) absAs fp_repAs;
     val castBs = map2 (curry HOLogic.mk_comp) absBs fp_repBs;
 
-    val rel_eqs = no_refl (map rel_eq_of_bnf fp_or_nesting_bnfs);
+    val fp_or_nesting_rel_eqs = no_refl (map rel_eq_of_bnf fp_or_nesting_bnfs);
+    val fp_or_nesting_rel_monos = map rel_mono_of_bnf fp_or_nesting_bnfs;
 
     val rel_xtor_co_induct_thm =
       mk_rel_xtor_co_induct_thm fp (map3 cast castAs castBs pre_rels) pre_phis rels phis xs ys
         xtors xtor's (mk_rel_xtor_co_induct_tactic fp abs_inverses rel_xtor_co_inducts rel_defs
-          rel_monos rel_eqs)
+          rel_monos fp_or_nesting_rel_eqs fp_or_nesting_rel_monos)
         lthy;
 
     val map_id0s = no_refl (map map_id0_of_bnf bnfs);
@@ -209,7 +210,8 @@
           in
             cterm_instantiate_pos cts rel_xtor_co_induct_thm
             |> singleton (Proof_Context.export names_lthy lthy)
-            |> unfold_thms lthy (@{thms eq_le_Grp_id_iff all_simps(1,2)[symmetric]} @ rel_eqs)
+            |> unfold_thms lthy (@{thms eq_le_Grp_id_iff all_simps(1,2)[symmetric]} @
+                fp_or_nesting_rel_eqs)
             |> funpow n (fn thm => thm RS spec)
             |> unfold_thms lthy (@{thm eq_alt} :: map rel_Grp_of_bnf bnfs @ map_id0s)
             |> unfold_thms lthy (@{thms vimage2p_id vimage2p_comp comp_apply comp_id
@@ -224,7 +226,8 @@
             val cts = NONE :: map (SOME o certify lthy) (map HOLogic.eq_const As);
           in
             cterm_instantiate_pos cts rel_xtor_co_induct_thm
-            |> unfold_thms lthy (@{thms le_fun_def le_bool_def all_simps(1,2)[symmetric]} @ rel_eqs)
+            |> unfold_thms lthy (@{thms le_fun_def le_bool_def all_simps(1,2)[symmetric]} @
+                fp_or_nesting_rel_eqs)
             |> funpow (2 * n) (fn thm => thm RS spec)
             |> Conv.fconv_rule (Object_Logic.atomize lthy)
             |> funpow n (fn thm => thm RS mp)

--- a/src/HOL/Tools/BNF/bnf_fp_n2m_tactics.ML	Thu Sep 18 16:47:40 2014 +0200
+++ b/src/HOL/Tools/BNF/bnf_fp_n2m_tactics.ML	Thu Sep 18 16:47:40 2014 +0200
@@ -8,7 +8,7 @@
 signature BNF_FP_N2M_TACTICS =
 sig
   val mk_rel_xtor_co_induct_tactic: BNF_Util.fp_kind -> thm list -> thm list -> thm list ->
-    thm list -> thm list -> {prems: thm list, context: Proof.context} -> tactic
+    thm list -> thm list -> thm list -> {prems: thm list, context: Proof.context} -> tactic
 end;
 
 structure BNF_FP_N2M_Tactics : BNF_FP_N2M_TACTICS =
@@ -20,11 +20,13 @@
 
 val vimage2p_unfolds = o_apply :: @{thms vimage2p_def};
 
-fun mk_rel_xtor_co_induct_tactic fp abs_inverses co_inducts0 rel_defs rel_monos nesting_rel_eqs
-  {context = ctxt, prems = raw_C_IHs} =
+fun mk_rel_xtor_co_induct_tactic fp abs_inverses co_inducts0 rel_defs rel_monos nesting_rel_eqs0
+  nesting_rel_monos0 {context = ctxt, prems = raw_C_IHs} =
   let
-    val co_inducts = map (unfold_thms ctxt
-      (vimage2p_unfolds @ @{thms prod.rel_eq sum.rel_eq} @ nesting_rel_eqs)) co_inducts0;
+    val nesting_rel_eqs = @{thms prod.rel_eq sum.rel_eq} @ nesting_rel_eqs0;
+    val nesting_rel_monos = map (fn thm => rotate_prems ~1 (thm RS @{thm predicate2D}))
+      (@{thms prod.rel_mono sum.rel_mono} @ nesting_rel_monos0);
+    val co_inducts = map (unfold_thms ctxt (vimage2p_unfolds @ nesting_rel_eqs)) co_inducts0;
     val unfolds = map (fn def =>
       unfold_thms ctxt (id_apply :: vimage2p_unfolds @ abs_inverses @ no_reflexive [def])) rel_defs;
     val folded_C_IHs = map (fn thm => thm RS @{thm spec2} RS mp) raw_C_IHs;
@@ -41,7 +43,9 @@
     HEADGOAL (CONJ_WRAP_GEN' (rtac @{thm context_conjI})
       (fn thm => rtac thm THEN_ALL_NEW (rotate_tac ~1 THEN'
          REPEAT_ALL_NEW (FIRST' [eresolve_tac C_IHs, eresolve_tac C_IH_monos,
-           rtac @{thm order_refl}, atac, resolve_tac co_inducts])))
+           SELECT_GOAL (unfold_thms_tac ctxt nesting_rel_eqs) THEN' rtac @{thm order_refl},
+           atac, resolve_tac co_inducts,
+           resolve_tac C_IH_monos THEN' REPEAT_ALL_NEW (eresolve_tac nesting_rel_monos)])))
     co_inducts)
   end;