Regenerate the test files

5 files changed, 418 insertions, 416 deletions

diff --git a/tests/hol4/betree/betreeMain_FunsScript.sml b/tests/hol4/betree/betreeMain_FunsScript.sml
index 03ff2671..b53c7b8d 100644
--- a/tests/hol4/betree/betreeMain_FunsScript.sml
+++ b/tests/hol4/betree/betreeMain_FunsScript.sml
@@ -279,22 +279,6 @@ val betree_leaf_split_back_def = Define ‘
     od
 ’
 
-val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
-  betree_node_lookup_in_bindings_fwd
-    (key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result =
-    (case bindings of
-    | BetreeListCons hd tl =>
-      let (i, i0) = hd in
-      if i = key
-      then Return (SOME i0)
-      else
-        if u64_gt i key
-        then Return NONE
-        else betree_node_lookup_in_bindings_fwd key tl
-    | BetreeListNil => Return NONE)
-’
-
 val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘
   (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
   betree_node_lookup_first_message_for_key_fwd
@@ -396,7 +380,51 @@ val [betree_node_apply_upserts_back_def] = DefineDiv ‘
     od
 ’
 
-val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def] = DefineDiv ‘
+val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
+  (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
+  betree_node_lookup_in_bindings_fwd
+    (key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result =
+    (case bindings of
+    | BetreeListCons hd tl =>
+      let (i, i0) = hd in
+      if i = key
+      then Return (SOME i0)
+      else
+        if u64_gt i key
+        then Return NONE
+        else betree_node_lookup_in_bindings_fwd key tl
+    | BetreeListNil => Return NONE)
+’
+
+val [betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def, betree_node_lookup_fwd_def, betree_node_lookup_back_def] = DefineDiv ‘
+  (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
+  (betree_internal_lookup_in_children_fwd
+     (self : betree_internal_t) (key : u64) (st : state) :
+     (state # u64 option) result
+     =
+    if u64_lt key self.betree_internal_pivot
+    then betree_node_lookup_fwd self.betree_internal_left key st
+    else betree_node_lookup_fwd self.betree_internal_right key st)
+  /\
+  
+  (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
+  (betree_internal_lookup_in_children_back
+     (self : betree_internal_t) (key : u64) (st : state) :
+     betree_internal_t result
+     =
+    if u64_lt key self.betree_internal_pivot
+    then (
+      do
+      n <- betree_node_lookup_back self.betree_internal_left key st;
+      Return (self with <| betree_internal_left := n |>)
+      od)
+    else (
+      do
+      n <- betree_node_lookup_back self.betree_internal_right key st;
+      Return (self with <| betree_internal_right := n |>)
+      od))
+  /\
+  
   (** [betree_main::betree::Node::{5}::lookup]: forward function *)
   (betree_node_lookup_fwd
      (self : betree_node_t) (key : u64) (st : state) :
@@ -468,8 +496,8 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
   /\
   
   (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
-  (betree_node_lookup_back
-     (self : betree_node_t) (key : u64) (st : state) : betree_node_t result =
+  betree_node_lookup_back
+    (self : betree_node_t) (key : u64) (st : state) : betree_node_t result =
     (case self of
     | BetreeNodeInternal node =>
       do
@@ -532,142 +560,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
       (_, bindings) <- betree_load_leaf_node_fwd node.betree_leaf_id st;
       _ <- betree_node_lookup_in_bindings_fwd key bindings;
       Return (BetreeNodeLeaf node)
-      od))
-  /\
-  
-  (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
-  (betree_internal_lookup_in_children_fwd
-     (self : betree_internal_t) (key : u64) (st : state) :
-     (state # u64 option) result
-     =
-    if u64_lt key self.betree_internal_pivot
-    then betree_node_lookup_fwd self.betree_internal_left key st
-    else betree_node_lookup_fwd self.betree_internal_right key st)
-  /\
-  
-  (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
-  betree_internal_lookup_in_children_back
-    (self : betree_internal_t) (key : u64) (st : state) :
-    betree_internal_t result
-    =
-    if u64_lt key self.betree_internal_pivot
-    then (
-      do
-      n <- betree_node_lookup_back self.betree_internal_left key st;
-      Return (self with <| betree_internal_left := n |>)
       od)
-    else (
-      do
-      n <- betree_node_lookup_back self.betree_internal_right key st;
-      Return (self with <| betree_internal_right := n |>)
-      od)
-’
-
-val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
-  betree_node_lookup_mut_in_bindings_fwd
-    (key : u64) (bindings : (u64 # u64) betree_list_t) :
-    (u64 # u64) betree_list_t result
-    =
-    (case bindings of
-    | BetreeListCons hd tl =>
-      let (i, i0) = hd in
-      if u64_ge i key
-      then Return (BetreeListCons (i, i0) tl)
-      else betree_node_lookup_mut_in_bindings_fwd key tl
-    | BetreeListNil => Return BetreeListNil)
-’
-
-val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
-  betree_node_lookup_mut_in_bindings_back
-    (key : u64) (bindings : (u64 # u64) betree_list_t)
-    (ret : (u64 # u64) betree_list_t) :
-    (u64 # u64) betree_list_t result
-    =
-    (case bindings of
-    | BetreeListCons hd tl =>
-      let (i, i0) = hd in
-      if u64_ge i key
-      then Return ret
-      else (
-        do
-        tl0 <- betree_node_lookup_mut_in_bindings_back key tl ret;
-        Return (BetreeListCons (i, i0) tl0)
-        od)
-    | BetreeListNil => Return ret)
-’
-
-val betree_node_apply_to_leaf_fwd_back_def = Define ‘
-  (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
-      (there is a single backward function, and the forward function returns ()) *)
-  betree_node_apply_to_leaf_fwd_back
-    (bindings : (u64 # u64) betree_list_t) (key : u64)
-    (new_msg : betree_message_t) :
-    (u64 # u64) betree_list_t result
-    =
-    do
-    bindings0 <- betree_node_lookup_mut_in_bindings_fwd key bindings;
-    b <- betree_list_head_has_key_fwd bindings0 key;
-    if b
-    then (
-      do
-      hd <- betree_list_pop_front_fwd bindings0;
-      (case new_msg of
-      | BetreeMessageInsert v =>
-        do
-        bindings1 <- betree_list_pop_front_back bindings0;
-        bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
-        betree_node_lookup_mut_in_bindings_back key bindings bindings2
-        od
-      | BetreeMessageDelete =>
-        do
-        bindings1 <- betree_list_pop_front_back bindings0;
-        betree_node_lookup_mut_in_bindings_back key bindings bindings1
-        od
-      | BetreeMessageUpsert s =>
-        let (_, i) = hd in
-        do
-        v <- betree_upsert_update_fwd (SOME i) s;
-        bindings1 <- betree_list_pop_front_back bindings0;
-        bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
-        betree_node_lookup_mut_in_bindings_back key bindings bindings2
-        od)
-      od)
-    else
-      (case new_msg of
-      | BetreeMessageInsert v =>
-        do
-        bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
-        betree_node_lookup_mut_in_bindings_back key bindings bindings1
-        od
-      | BetreeMessageDelete =>
-        betree_node_lookup_mut_in_bindings_back key bindings bindings0
-      | BetreeMessageUpsert s =>
-        do
-        v <- betree_upsert_update_fwd NONE s;
-        bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
-        betree_node_lookup_mut_in_bindings_back key bindings bindings1
-        od)
-    od
-’
-
-val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
-      (there is a single backward function, and the forward function returns ()) *)
-  betree_node_apply_messages_to_leaf_fwd_back
-    (bindings : (u64 # u64) betree_list_t)
-    (new_msgs : (u64 # betree_message_t) betree_list_t) :
-    (u64 # u64) betree_list_t result
-    =
-    (case new_msgs of
-    | BetreeListCons new_msg new_msgs_tl =>
-      let (i, m) = new_msg in
-      do
-      bindings0 <- betree_node_apply_to_leaf_fwd_back bindings i m;
-      betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
-      od
-    | BetreeListNil => Return bindings)
 ’
 
 val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘
@@ -811,7 +704,211 @@ val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘
     | BetreeListNil => Return msgs)
 ’
 
-val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, betree_internal_flush_fwd_def, betree_internal_flush_back_def] = DefineDiv ‘
+val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
+  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
+  betree_node_lookup_mut_in_bindings_fwd
+    (key : u64) (bindings : (u64 # u64) betree_list_t) :
+    (u64 # u64) betree_list_t result
+    =
+    (case bindings of
+    | BetreeListCons hd tl =>
+      let (i, i0) = hd in
+      if u64_ge i key
+      then Return (BetreeListCons (i, i0) tl)
+      else betree_node_lookup_mut_in_bindings_fwd key tl
+    | BetreeListNil => Return BetreeListNil)
+’
+
+val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
+  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
+  betree_node_lookup_mut_in_bindings_back
+    (key : u64) (bindings : (u64 # u64) betree_list_t)
+    (ret : (u64 # u64) betree_list_t) :
+    (u64 # u64) betree_list_t result
+    =
+    (case bindings of
+    | BetreeListCons hd tl =>
+      let (i, i0) = hd in
+      if u64_ge i key
+      then Return ret
+      else (
+        do
+        tl0 <- betree_node_lookup_mut_in_bindings_back key tl ret;
+        Return (BetreeListCons (i, i0) tl0)
+        od)
+    | BetreeListNil => Return ret)
+’
+
+val betree_node_apply_to_leaf_fwd_back_def = Define ‘
+  (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
+  betree_node_apply_to_leaf_fwd_back
+    (bindings : (u64 # u64) betree_list_t) (key : u64)
+    (new_msg : betree_message_t) :
+    (u64 # u64) betree_list_t result
+    =
+    do
+    bindings0 <- betree_node_lookup_mut_in_bindings_fwd key bindings;
+    b <- betree_list_head_has_key_fwd bindings0 key;
+    if b
+    then (
+      do
+      hd <- betree_list_pop_front_fwd bindings0;
+      (case new_msg of
+      | BetreeMessageInsert v =>
+        do
+        bindings1 <- betree_list_pop_front_back bindings0;
+        bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
+        betree_node_lookup_mut_in_bindings_back key bindings bindings2
+        od
+      | BetreeMessageDelete =>
+        do
+        bindings1 <- betree_list_pop_front_back bindings0;
+        betree_node_lookup_mut_in_bindings_back key bindings bindings1
+        od
+      | BetreeMessageUpsert s =>
+        let (_, i) = hd in
+        do
+        v <- betree_upsert_update_fwd (SOME i) s;
+        bindings1 <- betree_list_pop_front_back bindings0;
+        bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
+        betree_node_lookup_mut_in_bindings_back key bindings bindings2
+        od)
+      od)
+    else
+      (case new_msg of
+      | BetreeMessageInsert v =>
+        do
+        bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
+        betree_node_lookup_mut_in_bindings_back key bindings bindings1
+        od
+      | BetreeMessageDelete =>
+        betree_node_lookup_mut_in_bindings_back key bindings bindings0
+      | BetreeMessageUpsert s =>
+        do
+        v <- betree_upsert_update_fwd NONE s;
+        bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
+        betree_node_lookup_mut_in_bindings_back key bindings bindings1
+        od)
+    od
+’
+
+val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
+  (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
+  betree_node_apply_messages_to_leaf_fwd_back
+    (bindings : (u64 # u64) betree_list_t)
+    (new_msgs : (u64 # betree_message_t) betree_list_t) :
+    (u64 # u64) betree_list_t result
+    =
+    (case new_msgs of
+    | BetreeListCons new_msg new_msgs_tl =>
+      let (i, m) = new_msg in
+      do
+      bindings0 <- betree_node_apply_to_leaf_fwd_back bindings i m;
+      betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
+      od
+    | BetreeListNil => Return bindings)
+’
+
+val [betree_internal_flush_fwd_def, betree_internal_flush_back_def, betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def] = DefineDiv ‘
+  (** [betree_main::betree::Internal::{4}::flush]: forward function *)
+  (betree_internal_flush_fwd
+     (self : betree_internal_t) (params : betree_params_t)
+     (node_id_cnt : betree_node_id_counter_t)
+     (content : (u64 # betree_message_t) betree_list_t) (st : state) :
+     (state # (u64 # betree_message_t) betree_list_t) result
+     =
+    do
+    p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
+    let (msgs_left, msgs_right) = p in
+    do
+    len_left <- betree_list_len_fwd msgs_left;
+    if u64_ge len_left params.betree_params_min_flush_size
+    then (
+      do
+      (st0, _) <-
+        betree_node_apply_messages_fwd self.betree_internal_left params
+          node_id_cnt msgs_left st;
+      (_, node_id_cnt0) <-
+        betree_node_apply_messages_back self.betree_internal_left params
+          node_id_cnt msgs_left st;
+      len_right <- betree_list_len_fwd msgs_right;
+      if u64_ge len_right params.betree_params_min_flush_size
+      then (
+        do
+        (st1, _) <-
+          betree_node_apply_messages_fwd self.betree_internal_right params
+            node_id_cnt0 msgs_right st0;
+        _ <-
+          betree_node_apply_messages_back self.betree_internal_right params
+            node_id_cnt0 msgs_right st0;
+        Return (st1, BetreeListNil)
+        od)
+      else Return (st0, msgs_right)
+      od)
+    else (
+      do
+      (st0, _) <-
+        betree_node_apply_messages_fwd self.betree_internal_right params
+          node_id_cnt msgs_right st;
+      _ <-
+        betree_node_apply_messages_back self.betree_internal_right params
+          node_id_cnt msgs_right st;
+      Return (st0, msgs_left)
+      od)
+    od
+    od)
+  /\
+  
+  (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
+  (betree_internal_flush_back
+     (self : betree_internal_t) (params : betree_params_t)
+     (node_id_cnt : betree_node_id_counter_t)
+     (content : (u64 # betree_message_t) betree_list_t) (st : state) :
+     (betree_internal_t # betree_node_id_counter_t) result
+     =
+    do
+    p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
+    let (msgs_left, msgs_right) = p in
+    do
+    len_left <- betree_list_len_fwd msgs_left;
+    if u64_ge len_left params.betree_params_min_flush_size
+    then (
+      do
+      (st0, _) <-
+        betree_node_apply_messages_fwd self.betree_internal_left params
+          node_id_cnt msgs_left st;
+      (n, node_id_cnt0) <-
+        betree_node_apply_messages_back self.betree_internal_left params
+          node_id_cnt msgs_left st;
+      len_right <- betree_list_len_fwd msgs_right;
+      if u64_ge len_right params.betree_params_min_flush_size
+      then (
+        do
+        (n0, node_id_cnt1) <-
+          betree_node_apply_messages_back self.betree_internal_right params
+            node_id_cnt0 msgs_right st0;
+        Return
+          (self
+             with
+             <|
+             betree_internal_left := n; betree_internal_right := n0
+             |>, node_id_cnt1)
+        od)
+      else Return (self with <| betree_internal_left := n |>, node_id_cnt0)
+      od)
+    else (
+      do
+      (n, node_id_cnt0) <-
+        betree_node_apply_messages_back self.betree_internal_right params
+          node_id_cnt msgs_right st;
+      Return (self with <| betree_internal_right := n |>, node_id_cnt0)
+      od)
+    od
+    od)
+  /\
+  
   (** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
   (betree_node_apply_messages_fwd
      (self : betree_node_t) (params : betree_params_t)
@@ -868,12 +965,12 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
   /\
   
   (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
-  (betree_node_apply_messages_back
-     (self : betree_node_t) (params : betree_params_t)
-     (node_id_cnt : betree_node_id_counter_t)
-     (msgs : (u64 # betree_message_t) betree_list_t) (st : state) :
-     (betree_node_t # betree_node_id_counter_t) result
-     =
+  betree_node_apply_messages_back
+    (self : betree_node_t) (params : betree_params_t)
+    (node_id_cnt : betree_node_id_counter_t)
+    (msgs : (u64 # betree_message_t) betree_list_t) (st : state) :
+    (betree_node_t # betree_node_id_counter_t) result
+    =
     (case self of
     | BetreeNodeInternal node =>
       do
@@ -921,104 +1018,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
         Return (BetreeNodeLeaf (node with <| betree_leaf_size := len |>),
           node_id_cnt)
         od)
-      od))
-  /\
-  
-  (** [betree_main::betree::Internal::{4}::flush]: forward function *)
-  (betree_internal_flush_fwd
-     (self : betree_internal_t) (params : betree_params_t)
-     (node_id_cnt : betree_node_id_counter_t)
-     (content : (u64 # betree_message_t) betree_list_t) (st : state) :
-     (state # (u64 # betree_message_t) betree_list_t) result
-     =
-    do
-    p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
-    let (msgs_left, msgs_right) = p in
-    do
-    len_left <- betree_list_len_fwd msgs_left;
-    if u64_ge len_left params.betree_params_min_flush_size
-    then (
-      do
-      (st0, _) <-
-        betree_node_apply_messages_fwd self.betree_internal_left params
-          node_id_cnt msgs_left st;
-      (_, node_id_cnt0) <-
-        betree_node_apply_messages_back self.betree_internal_left params
-          node_id_cnt msgs_left st;
-      len_right <- betree_list_len_fwd msgs_right;
-      if u64_ge len_right params.betree_params_min_flush_size
-      then (
-        do
-        (st1, _) <-
-          betree_node_apply_messages_fwd self.betree_internal_right params
-            node_id_cnt0 msgs_right st0;
-        _ <-
-          betree_node_apply_messages_back self.betree_internal_right params
-            node_id_cnt0 msgs_right st0;
-        Return (st1, BetreeListNil)
-        od)
-      else Return (st0, msgs_right)
-      od)
-    else (
-      do
-      (st0, _) <-
-        betree_node_apply_messages_fwd self.betree_internal_right params
-          node_id_cnt msgs_right st;
-      _ <-
-        betree_node_apply_messages_back self.betree_internal_right params
-          node_id_cnt msgs_right st;
-      Return (st0, msgs_left)
       od)
-    od
-    od)
-  /\
-  
-  (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
-  betree_internal_flush_back
-    (self : betree_internal_t) (params : betree_params_t)
-    (node_id_cnt : betree_node_id_counter_t)
-    (content : (u64 # betree_message_t) betree_list_t) (st : state) :
-    (betree_internal_t # betree_node_id_counter_t) result
-    =
-    do
-    p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
-    let (msgs_left, msgs_right) = p in
-    do
-    len_left <- betree_list_len_fwd msgs_left;
-    if u64_ge len_left params.betree_params_min_flush_size
-    then (
-      do
-      (st0, _) <-
-        betree_node_apply_messages_fwd self.betree_internal_left params
-          node_id_cnt msgs_left st;
-      (n, node_id_cnt0) <-
-        betree_node_apply_messages_back self.betree_internal_left params
-          node_id_cnt msgs_left st;
-      len_right <- betree_list_len_fwd msgs_right;
-      if u64_ge len_right params.betree_params_min_flush_size
-      then (
-        do
-        (n0, node_id_cnt1) <-
-          betree_node_apply_messages_back self.betree_internal_right params
-            node_id_cnt0 msgs_right st0;
-        Return
-          (self
-             with
-             <|
-             betree_internal_left := n; betree_internal_right := n0
-             |>, node_id_cnt1)
-        od)
-      else Return (self with <| betree_internal_left := n |>, node_id_cnt0)
-      od)
-    else (
-      do
-      (n, node_id_cnt0) <-
-        betree_node_apply_messages_back self.betree_internal_right params
-          node_id_cnt msgs_right st;
-      Return (self with <| betree_internal_right := n |>, node_id_cnt0)
-      od)
-    od
-    od
 ’
 
 val betree_node_apply_fwd_def = Define ‘
diff --git a/tests/hol4/betree/betreeMain_TypesScript.sml b/tests/hol4/betree/betreeMain_TypesScript.sml
index c43421c2..779f6abb 100644
--- a/tests/hol4/betree/betreeMain_TypesScript.sml
+++ b/tests/hol4/betree/betreeMain_TypesScript.sml
@@ -31,12 +31,6 @@ Datatype:
 End
 
 Datatype:
-  (** [betree_main::betree::Node] *)
-  betree_node_t =
-  | BetreeNodeInternal betree_internal_t
-  | BetreeNodeLeaf betree_leaf_t
-  ;
-  
   (** [betree_main::betree::Internal] *)
   betree_internal_t =
   <|
@@ -45,6 +39,12 @@ Datatype:
     betree_internal_left : betree_node_t;
     betree_internal_right : betree_node_t;
   |>
+  ;
+  
+  (** [betree_main::betree::Node] *)
+  betree_node_t =
+  | BetreeNodeInternal betree_internal_t
+  | BetreeNodeLeaf betree_leaf_t
 End
 
 Datatype:
diff --git a/tests/hol4/betree/betreeMain_TypesTheory.sig b/tests/hol4/betree/betreeMain_TypesTheory.sig
index a451eae9..cffe6afb 100644
--- a/tests/hol4/betree/betreeMain_TypesTheory.sig
+++ b/tests/hol4/betree/betreeMain_TypesTheory.sig
@@ -22,6 +22,7 @@ sig
     val betree_internal_t_betree_internal_right : thm
     val betree_internal_t_betree_internal_right_fupd : thm
     val betree_internal_t_case_def : thm
+    val betree_internal_t_size_def : thm
     val betree_leaf_t_TY_DEF : thm
     val betree_leaf_t_betree_leaf_id : thm
     val betree_leaf_t_betree_leaf_id_fupd : thm
@@ -42,7 +43,6 @@ sig
     val betree_node_id_counter_t_size_def : thm
     val betree_node_t_TY_DEF : thm
     val betree_node_t_case_def : thm
-    val betree_node_t_size_def : thm
     val betree_params_t_TY_DEF : thm
     val betree_params_t_betree_params_min_flush_size : thm
     val betree_params_t_betree_params_min_flush_size_fupd : thm
@@ -177,11 +177,11 @@ sig
     val betree_upsert_fun_state_t_induction : thm
     val betree_upsert_fun_state_t_nchotomy : thm
     val datatype_betree_be_tree_t : thm
+    val datatype_betree_internal_t : thm
     val datatype_betree_leaf_t : thm
     val datatype_betree_list_t : thm
     val datatype_betree_message_t : thm
     val datatype_betree_node_id_counter_t : thm
-    val datatype_betree_node_t : thm
     val datatype_betree_params_t : thm
     val datatype_betree_upsert_fun_state_t : thm
   
@@ -253,30 +253,30 @@ sig
       
       ⊢ ∃rep.
           TYPE_DEFINITION
-            (λa1'.
-                 ∀ $var$('betree_node_t') $var$('betree_internal_t').
+            (λa0'.
+                 ∀ $var$('betree_internal_t') $var$('betree_node_t').
                    (∀a0'.
-                      (∃a. a0' =
-                           (λa.
-                                ind_type$CONSTR 0 (ARB,ARB,ARB)
-                                  (ind_type$FCONS a (λn. ind_type$BOTTOM)))
-                             a ∧ $var$('betree_internal_t') a) ∨
-                      (∃a. a0' =
-                           (λa.
-                                ind_type$CONSTR (SUC 0) (a,ARB,ARB)
-                                  (λn. ind_type$BOTTOM)) a) ⇒
-                      $var$('betree_node_t') a0') ∧
-                   (∀a1'.
                       (∃a0 a1 a2 a3.
-                         a1' =
+                         a0' =
                          (λa0 a1 a2 a3.
-                              ind_type$CONSTR (SUC (SUC 0)) (ARB,a0,a1)
+                              ind_type$CONSTR 0 (a0,a1,ARB)
                                 (ind_type$FCONS a2
                                    (ind_type$FCONS a3 (λn. ind_type$BOTTOM))))
                            a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧
                          $var$('betree_node_t') a3) ⇒
-                      $var$('betree_internal_t') a1') ⇒
-                   $var$('betree_internal_t') a1') rep
+                      $var$('betree_internal_t') a0') ∧
+                   (∀a1'.
+                      (∃a. a1' =
+                           (λa.
+                                ind_type$CONSTR (SUC 0) (ARB,ARB,ARB)
+                                  (ind_type$FCONS a (λn. ind_type$BOTTOM)))
+                             a ∧ $var$('betree_internal_t') a) ∨
+                      (∃a. a1' =
+                           (λa.
+                                ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a)
+                                  (λn. ind_type$BOTTOM)) a) ⇒
+                      $var$('betree_node_t') a1') ⇒
+                   $var$('betree_internal_t') a0') rep
    
    [betree_internal_t_betree_internal_id]  Definition
       
@@ -329,6 +329,16 @@ sig
           betree_internal_t_CASE (betree_internal_t a0 a1 a2 a3) f =
           f a0 a1 a2 a3
    
+   [betree_internal_t_size_def]  Definition
+      
+      ⊢ (∀a0 a1 a2 a3.
+           betree_internal_t_size (betree_internal_t a0 a1 a2 a3) =
+           1 + (betree_node_t_size a2 + betree_node_t_size a3)) ∧
+        (∀a. betree_node_t_size (BetreeNodeInternal a) =
+             1 + betree_internal_t_size a) ∧
+        ∀a. betree_node_t_size (BetreeNodeLeaf a) =
+            1 + betree_leaf_t_size a
+   
    [betree_leaf_t_TY_DEF]  Definition
       
       ⊢ ∃rep.
@@ -479,46 +489,36 @@ sig
       
       ⊢ ∃rep.
           TYPE_DEFINITION
-            (λa0'.
-                 ∀ $var$('betree_node_t') $var$('betree_internal_t').
+            (λa1'.
+                 ∀ $var$('betree_internal_t') $var$('betree_node_t').
                    (∀a0'.
-                      (∃a. a0' =
-                           (λa.
-                                ind_type$CONSTR 0 (ARB,ARB,ARB)
-                                  (ind_type$FCONS a (λn. ind_type$BOTTOM)))
-                             a ∧ $var$('betree_internal_t') a) ∨
-                      (∃a. a0' =
-                           (λa.
-                                ind_type$CONSTR (SUC 0) (a,ARB,ARB)
-                                  (λn. ind_type$BOTTOM)) a) ⇒
-                      $var$('betree_node_t') a0') ∧
-                   (∀a1'.
                       (∃a0 a1 a2 a3.
-                         a1' =
+                         a0' =
                          (λa0 a1 a2 a3.
-                              ind_type$CONSTR (SUC (SUC 0)) (ARB,a0,a1)
+                              ind_type$CONSTR 0 (a0,a1,ARB)
                                 (ind_type$FCONS a2
                                    (ind_type$FCONS a3 (λn. ind_type$BOTTOM))))
                            a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧
                          $var$('betree_node_t') a3) ⇒
-                      $var$('betree_internal_t') a1') ⇒
-                   $var$('betree_node_t') a0') rep
+                      $var$('betree_internal_t') a0') ∧
+                   (∀a1'.
+                      (∃a. a1' =
+                           (λa.
+                                ind_type$CONSTR (SUC 0) (ARB,ARB,ARB)
+                                  (ind_type$FCONS a (λn. ind_type$BOTTOM)))
+                             a ∧ $var$('betree_internal_t') a) ∨
+                      (∃a. a1' =
+                           (λa.
+                                ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a)
+                                  (λn. ind_type$BOTTOM)) a) ⇒
+                      $var$('betree_node_t') a1') ⇒
+                   $var$('betree_node_t') a1') rep
    
    [betree_node_t_case_def]  Definition
       
       ⊢ (∀a f f1. betree_node_t_CASE (BetreeNodeInternal a) f f1 = f a) ∧
         ∀a f f1. betree_node_t_CASE (BetreeNodeLeaf a) f f1 = f1 a
    
-   [betree_node_t_size_def]  Definition
-      
-      ⊢ (∀a. betree_node_t_size (BetreeNodeInternal a) =
-             1 + betree_internal_t_size a) ∧
-        (∀a. betree_node_t_size (BetreeNodeLeaf a) =
-             1 + betree_leaf_t_size a) ∧
-        ∀a0 a1 a2 a3.
-          betree_internal_t_size (betree_internal_t a0 a1 a2 a3) =
-          1 + (betree_node_t_size a2 + betree_node_t_size a3)
-   
    [betree_params_t_TY_DEF]  Definition
       
       ⊢ ∃rep.
@@ -883,11 +883,11 @@ sig
    [betree_internal_t_Axiom]  Theorem
       
       ⊢ ∀f0 f1 f2. ∃fn0 fn1.
-          (∀a. fn0 (BetreeNodeInternal a) = f0 a (fn1 a)) ∧
-          (∀a. fn0 (BetreeNodeLeaf a) = f1 a) ∧
-          ∀a0 a1 a2 a3.
-            fn1 (betree_internal_t a0 a1 a2 a3) =
-            f2 a0 a1 a2 a3 (fn0 a2) (fn0 a3)
+          (∀a0 a1 a2 a3.
+             fn0 (betree_internal_t a0 a1 a2 a3) =
+             f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧
+          (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧
+          ∀a. fn1 (BetreeNodeLeaf a) = f2 a
    
    [betree_internal_t_accessors]  Theorem
       
@@ -1130,9 +1130,9 @@ sig
    [betree_internal_t_induction]  Theorem
       
       ⊢ ∀P0 P1.
-          (∀b. P1 b ⇒ P0 (BetreeNodeInternal b)) ∧
-          (∀b. P0 (BetreeNodeLeaf b)) ∧
-          (∀b b0. P0 b ∧ P0 b0 ⇒ ∀u u0. P1 (betree_internal_t u0 u b b0)) ⇒
+          (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧
+          (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧
+          (∀b. P1 (BetreeNodeLeaf b)) ⇒
           (∀b. P0 b) ∧ ∀b. P1 b
    
    [betree_internal_t_literal_11]  Theorem
@@ -1472,11 +1472,11 @@ sig
    [betree_node_t_Axiom]  Theorem
       
       ⊢ ∀f0 f1 f2. ∃fn0 fn1.
-          (∀a. fn0 (BetreeNodeInternal a) = f0 a (fn1 a)) ∧
-          (∀a. fn0 (BetreeNodeLeaf a) = f1 a) ∧
-          ∀a0 a1 a2 a3.
-            fn1 (betree_internal_t a0 a1 a2 a3) =
-            f2 a0 a1 a2 a3 (fn0 a2) (fn0 a3)
+          (∀a0 a1 a2 a3.
+             fn0 (betree_internal_t a0 a1 a2 a3) =
+             f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧
+          (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧
+          ∀a. fn1 (BetreeNodeLeaf a) = f2 a
    
    [betree_node_t_case_cong]  Theorem
       
@@ -1498,9 +1498,9 @@ sig
    [betree_node_t_induction]  Theorem
       
       ⊢ ∀P0 P1.
-          (∀b. P1 b ⇒ P0 (BetreeNodeInternal b)) ∧
-          (∀b. P0 (BetreeNodeLeaf b)) ∧
-          (∀b b0. P0 b ∧ P0 b0 ⇒ ∀u u0. P1 (betree_internal_t u0 u b b0)) ⇒
+          (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧
+          (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧
+          (∀b. P1 (BetreeNodeLeaf b)) ⇒
           (∀b. P0 b) ∧ ∀b. P1 b
    
    [betree_node_t_nchotomy]  Theorem
@@ -1706,6 +1706,14 @@ sig
           (record betree_be_tree_t betree_be_tree_params
              betree_be_tree_node_id_cnt betree_be_tree_root)
    
+   [datatype_betree_internal_t]  Theorem
+      
+      ⊢ DATATYPE
+          (record betree_internal_t betree_internal_id
+             betree_internal_pivot betree_internal_left
+             betree_internal_right ∧
+           betree_node_t BetreeNodeInternal BetreeNodeLeaf)
+   
    [datatype_betree_leaf_t]  Theorem
       
       ⊢ DATATYPE (record betree_leaf_t betree_leaf_id betree_leaf_size)
@@ -1726,14 +1734,6 @@ sig
           (record betree_node_id_counter_t
              betree_node_id_counter_next_node_id)
    
-   [datatype_betree_node_t]  Theorem
-      
-      ⊢ DATATYPE
-          (betree_node_t BetreeNodeInternal BetreeNodeLeaf ∧
-           record betree_internal_t betree_internal_id
-             betree_internal_pivot betree_internal_left
-             betree_internal_right)
-   
    [datatype_betree_params_t]  Theorem
       
       ⊢ DATATYPE
diff --git a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
index 66614c3f..1b2d6121 100644
--- a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
+++ b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
@@ -279,11 +279,11 @@ val test_char_fwd_def = Define ‘
 ’
 
 Datatype:
-  (** [no_nested_borrows::NodeElem] *)
-  node_elem_t = | NodeElemCons tree_t node_elem_t | NodeElemNil ;
-  
   (** [no_nested_borrows::Tree] *)
-  tree_t = | TreeLeaf 't | TreeNode 't node_elem_t tree_t
+  tree_t = | TreeLeaf 't | TreeNode 't node_elem_t tree_t ;
+  
+  (** [no_nested_borrows::NodeElem] *)
+  node_elem_t = | NodeElemCons tree_t node_elem_t | NodeElemNil
 End
 
 val [list_length_fwd_def] = DefineDiv ‘
diff --git a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig
index c0ff4e09..67368e38 100644
--- a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig
+++ b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig
@@ -47,7 +47,6 @@ sig
     val new_tuple3_fwd_def : thm
     val node_elem_t_TY_DEF : thm
     val node_elem_t_case_def : thm
-    val node_elem_t_size_def : thm
     val one_t_TY_DEF : thm
     val one_t_case_def : thm
     val one_t_size_def : thm
@@ -97,6 +96,7 @@ sig
     val test_weird_borrows1_fwd_def : thm
     val tree_t_TY_DEF : thm
     val tree_t_case_def : thm
+    val tree_t_size_def : thm
   
   (*  Theorems  *)
     val EXISTS_pair_t : thm
@@ -108,12 +108,12 @@ sig
     val datatype_empty_enum_t : thm
     val datatype_enum_t : thm
     val datatype_list_t : thm
-    val datatype_node_elem_t : thm
     val datatype_one_t : thm
     val datatype_pair_t : thm
     val datatype_struct_with_pair_t : thm
     val datatype_struct_with_tuple_t : thm
     val datatype_sum_t : thm
+    val datatype_tree_t : thm
     val empty_enum_t2num_11 : thm
     val empty_enum_t2num_ONTO : thm
     val empty_enum_t2num_num2empty_enum_t : thm
@@ -491,52 +491,41 @@ sig
       
       ⊢ ∃rep.
           TYPE_DEFINITION
-            (λa0'.
-                 ∀ $var$('node_elem_t') $var$('tree_t').
+            (λa1'.
+                 ∀ $var$('tree_t') $var$('node_elem_t').
                    (∀a0'.
-                      (∃a0 a1.
-                         a0' =
-                         (λa0 a1.
-                              ind_type$CONSTR 0 ARB
-                                (ind_type$FCONS a0
-                                   (ind_type$FCONS a1 (λn. ind_type$BOTTOM))))
-                           a0 a1 ∧ $var$('tree_t') a0 ∧
-                         $var$('node_elem_t') a1) ∨
-                      a0' =
-                      ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒
-                      $var$('node_elem_t') a0') ∧
-                   (∀a1'.
-                      (∃a. a1' =
-                           (λa.
-                                ind_type$CONSTR (SUC (SUC 0)) a
-                                  (λn. ind_type$BOTTOM)) a) ∨
+                      (∃a. a0' =
+                           (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM))
+                             a) ∨
                       (∃a0 a1 a2.
-                         a1' =
+                         a0' =
                          (λa0 a1 a2.
-                              ind_type$CONSTR (SUC (SUC (SUC 0))) a0
+                              ind_type$CONSTR (SUC 0) a0
                                 (ind_type$FCONS a1
                                    (ind_type$FCONS a2 (λn. ind_type$BOTTOM))))
                            a0 a1 a2 ∧ $var$('node_elem_t') a1 ∧
                          $var$('tree_t') a2) ⇒
-                      $var$('tree_t') a1') ⇒
-                   $var$('node_elem_t') a0') rep
+                      $var$('tree_t') a0') ∧
+                   (∀a1'.
+                      (∃a0 a1.
+                         a1' =
+                         (λa0 a1.
+                              ind_type$CONSTR (SUC (SUC 0)) ARB
+                                (ind_type$FCONS a0
+                                   (ind_type$FCONS a1 (λn. ind_type$BOTTOM))))
+                           a0 a1 ∧ $var$('tree_t') a0 ∧
+                         $var$('node_elem_t') a1) ∨
+                      a1' =
+                      ind_type$CONSTR (SUC (SUC (SUC 0))) ARB
+                        (λn. ind_type$BOTTOM) ⇒
+                      $var$('node_elem_t') a1') ⇒
+                   $var$('node_elem_t') a1') rep
    
    [node_elem_t_case_def]  Definition
       
       ⊢ (∀a0 a1 f v. node_elem_t_CASE (NodeElemCons a0 a1) f v = f a0 a1) ∧
         ∀f v. node_elem_t_CASE NodeElemNil f v = v
    
-   [node_elem_t_size_def]  Definition
-      
-      ⊢ (∀f a0 a1.
-           node_elem_t_size f (NodeElemCons a0 a1) =
-           1 + (tree_t_size f a0 + node_elem_t_size f a1)) ∧
-        (∀f. node_elem_t_size f NodeElemNil = 0) ∧
-        (∀f a. tree_t_size f (TreeLeaf a) = 1 + f a) ∧
-        ∀f a0 a1 a2.
-          tree_t_size f (TreeNode a0 a1 a2) =
-          1 + (f a0 + (node_elem_t_size f a1 + tree_t_size f a2))
-   
    [one_t_TY_DEF]  Definition
       
       ⊢ ∃rep.
@@ -923,41 +912,52 @@ sig
       
       ⊢ ∃rep.
           TYPE_DEFINITION
-            (λa1'.
-                 ∀ $var$('node_elem_t') $var$('tree_t').
+            (λa0'.
+                 ∀ $var$('tree_t') $var$('node_elem_t').
                    (∀a0'.
-                      (∃a0 a1.
-                         a0' =
-                         (λa0 a1.
-                              ind_type$CONSTR 0 ARB
-                                (ind_type$FCONS a0
-                                   (ind_type$FCONS a1 (λn. ind_type$BOTTOM))))
-                           a0 a1 ∧ $var$('tree_t') a0 ∧
-                         $var$('node_elem_t') a1) ∨
-                      a0' =
-                      ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒
-                      $var$('node_elem_t') a0') ∧
-                   (∀a1'.
-                      (∃a. a1' =
-                           (λa.
-                                ind_type$CONSTR (SUC (SUC 0)) a
-                                  (λn. ind_type$BOTTOM)) a) ∨
+                      (∃a. a0' =
+                           (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM))
+                             a) ∨
                       (∃a0 a1 a2.
-                         a1' =
+                         a0' =
                          (λa0 a1 a2.
-                              ind_type$CONSTR (SUC (SUC (SUC 0))) a0
+                              ind_type$CONSTR (SUC 0) a0
                                 (ind_type$FCONS a1
                                    (ind_type$FCONS a2 (λn. ind_type$BOTTOM))))
                            a0 a1 a2 ∧ $var$('node_elem_t') a1 ∧
                          $var$('tree_t') a2) ⇒
-                      $var$('tree_t') a1') ⇒
-                   $var$('tree_t') a1') rep
+                      $var$('tree_t') a0') ∧
+                   (∀a1'.
+                      (∃a0 a1.
+                         a1' =
+                         (λa0 a1.
+                              ind_type$CONSTR (SUC (SUC 0)) ARB
+                                (ind_type$FCONS a0
+                                   (ind_type$FCONS a1 (λn. ind_type$BOTTOM))))
+                           a0 a1 ∧ $var$('tree_t') a0 ∧
+                         $var$('node_elem_t') a1) ∨
+                      a1' =
+                      ind_type$CONSTR (SUC (SUC (SUC 0))) ARB
+                        (λn. ind_type$BOTTOM) ⇒
+                      $var$('node_elem_t') a1') ⇒
+                   $var$('tree_t') a0') rep
    
    [tree_t_case_def]  Definition
       
       ⊢ (∀a f f1. tree_t_CASE (TreeLeaf a) f f1 = f a) ∧
         ∀a0 a1 a2 f f1. tree_t_CASE (TreeNode a0 a1 a2) f f1 = f1 a0 a1 a2
    
+   [tree_t_size_def]  Definition
+      
+      ⊢ (∀f a. tree_t_size f (TreeLeaf a) = 1 + f a) ∧
+        (∀f a0 a1 a2.
+           tree_t_size f (TreeNode a0 a1 a2) =
+           1 + (f a0 + (node_elem_t_size f a1 + tree_t_size f a2))) ∧
+        (∀f a0 a1.
+           node_elem_t_size f (NodeElemCons a0 a1) =
+           1 + (tree_t_size f a0 + node_elem_t_size f a1)) ∧
+        ∀f. node_elem_t_size f NodeElemNil = 0
+   
    [EXISTS_pair_t]  Theorem
       
       ⊢ ∀P. (∃p. P p) ⇔ ∃t0 t. P <|pair_x := t0; pair_y := t|>
@@ -994,11 +994,6 @@ sig
       
       ⊢ DATATYPE (list_t ListCons ListNil)
    
-   [datatype_node_elem_t]  Theorem
-      
-      ⊢ DATATYPE
-          (node_elem_t NodeElemCons NodeElemNil ∧ tree_t TreeLeaf TreeNode)
-   
    [datatype_one_t]  Theorem
       
       ⊢ DATATYPE (one_t OneOne)
@@ -1019,6 +1014,11 @@ sig
       
       ⊢ DATATYPE (sum_t SumLeft SumRight)
    
+   [datatype_tree_t]  Theorem
+      
+      ⊢ DATATYPE
+          (tree_t TreeLeaf TreeNode ∧ node_elem_t NodeElemCons NodeElemNil)
+   
    [empty_enum_t2num_11]  Theorem
       
       ⊢ ∀a a'. empty_enum_t2num a = empty_enum_t2num a' ⇔ a = a'
@@ -1167,10 +1167,11 @@ sig
    [node_elem_t_Axiom]  Theorem
       
       ⊢ ∀f0 f1 f2 f3. ∃fn0 fn1.
-          (∀a0 a1. fn0 (NodeElemCons a0 a1) = f0 a0 a1 (fn1 a0) (fn0 a1)) ∧
-          fn0 NodeElemNil = f1 ∧ (∀a. fn1 (TreeLeaf a) = f2 a) ∧
-          ∀a0 a1 a2.
-            fn1 (TreeNode a0 a1 a2) = f3 a0 a1 a2 (fn0 a1) (fn1 a2)
+          (∀a. fn0 (TreeLeaf a) = f0 a) ∧
+          (∀a0 a1 a2.
+             fn0 (TreeNode a0 a1 a2) = f1 a0 a1 a2 (fn1 a1) (fn0 a2)) ∧
+          (∀a0 a1. fn1 (NodeElemCons a0 a1) = f2 a0 a1 (fn0 a0) (fn1 a1)) ∧
+          fn1 NodeElemNil = f3
    
    [node_elem_t_case_cong]  Theorem
       
@@ -1192,10 +1193,10 @@ sig
    [node_elem_t_induction]  Theorem
       
       ⊢ ∀P0 P1.
-          (∀t n. P1 t ∧ P0 n ⇒ P0 (NodeElemCons t n)) ∧ P0 NodeElemNil ∧
-          (∀t. P1 (TreeLeaf t)) ∧
-          (∀n t. P0 n ∧ P1 t ⇒ ∀t0. P1 (TreeNode t0 n t)) ⇒
-          (∀n. P0 n) ∧ ∀t. P1 t
+          (∀t. P0 (TreeLeaf t)) ∧
+          (∀n t. P1 n ∧ P0 t ⇒ ∀t0. P0 (TreeNode t0 n t)) ∧
+          (∀t n. P0 t ∧ P1 n ⇒ P1 (NodeElemCons t n)) ∧ P1 NodeElemNil ⇒
+          (∀t. P0 t) ∧ ∀n. P1 n
    
    [node_elem_t_nchotomy]  Theorem
       
@@ -1557,10 +1558,11 @@ sig
    [tree_t_Axiom]  Theorem
       
       ⊢ ∀f0 f1 f2 f3. ∃fn0 fn1.
-          (∀a0 a1. fn0 (NodeElemCons a0 a1) = f0 a0 a1 (fn1 a0) (fn0 a1)) ∧
-          fn0 NodeElemNil = f1 ∧ (∀a. fn1 (TreeLeaf a) = f2 a) ∧
-          ∀a0 a1 a2.
-            fn1 (TreeNode a0 a1 a2) = f3 a0 a1 a2 (fn0 a1) (fn1 a2)
+          (∀a. fn0 (TreeLeaf a) = f0 a) ∧
+          (∀a0 a1 a2.
+             fn0 (TreeNode a0 a1 a2) = f1 a0 a1 a2 (fn1 a1) (fn0 a2)) ∧
+          (∀a0 a1. fn1 (NodeElemCons a0 a1) = f2 a0 a1 (fn0 a0) (fn1 a1)) ∧
+          fn1 NodeElemNil = f3
    
    [tree_t_case_cong]  Theorem
       
@@ -1582,10 +1584,10 @@ sig
    [tree_t_induction]  Theorem
       
       ⊢ ∀P0 P1.
-          (∀t n. P1 t ∧ P0 n ⇒ P0 (NodeElemCons t n)) ∧ P0 NodeElemNil ∧
-          (∀t. P1 (TreeLeaf t)) ∧
-          (∀n t. P0 n ∧ P1 t ⇒ ∀t0. P1 (TreeNode t0 n t)) ⇒
-          (∀n. P0 n) ∧ ∀t. P1 t
+          (∀t. P0 (TreeLeaf t)) ∧
+          (∀n t. P1 n ∧ P0 t ⇒ ∀t0. P0 (TreeNode t0 n t)) ∧
+          (∀t n. P0 t ∧ P1 n ⇒ P1 (NodeElemCons t n)) ∧ P1 NodeElemNil ⇒
+          (∀t. P0 t) ∧ ∀n. P1 n
    
    [tree_t_nchotomy]  Theorem