Start using namespaces in the Lean backend

38 files changed, 682 insertions, 614 deletions

diff --git a/tests/coq/betree/BetreeMain_Opaque.v b/tests/coq/betree/BetreeMain_Opaque.v
index 08ab530a..51321f56 100644
--- a/tests/coq/betree/BetreeMain_Opaque.v
+++ b/tests/coq/betree/BetreeMain_Opaque.v
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
index 6152b94b..e1e7fe2b 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
diff --git a/tests/coq/misc/External_Opaque.v b/tests/coq/misc/External_Opaque.v
index d60251e0..5ee65277 100644
--- a/tests/coq/misc/External_Opaque.v
+++ b/tests/coq/misc/External_Opaque.v
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
diff --git a/tests/fstar/betree/BetreeMain.Opaque.fsti b/tests/fstar/betree/BetreeMain.Opaque.fsti
index dc49601a..dfbd73d6 100644
--- a/tests/fstar/betree/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree/BetreeMain.Opaque.fsti
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 module BetreeMain.Opaque
 open Primitives
 include BetreeMain.Types
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
index dc49601a..dfbd73d6 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 module BetreeMain.Opaque
 open Primitives
 include BetreeMain.Types
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
index 6e54ea10..6e6a0e2b 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
 module HashmapMain.Opaque
 open Primitives
 include HashmapMain.Types
diff --git a/tests/fstar/misc/External.Opaque.fsti b/tests/fstar/misc/External.Opaque.fsti
index 7d86405a..356d5fc4 100644
--- a/tests/fstar/misc/External.Opaque.fsti
+++ b/tests/fstar/misc/External.Opaque.fsti
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
 module External.Opaque
 open Primitives
 include External.Types
diff --git a/tests/hol4/betree/betreeMain_OpaqueScript.sml b/tests/hol4/betree/betreeMain_OpaqueScript.sml
index a6f0cf15..10d67cca 100644
--- a/tests/hol4/betree/betreeMain_OpaqueScript.sml
+++ b/tests/hol4/betree/betreeMain_OpaqueScript.sml
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 open primitivesLib divDefLib
 open betreeMain_TypesTheory
 
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
index 5f6bcbb4..c38eca01 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
 open primitivesLib divDefLib
 open hashmapMain_TypesTheory
 
diff --git a/tests/hol4/misc-external/external_OpaqueScript.sml b/tests/hol4/misc-external/external_OpaqueScript.sml
index e2fd281d..02efc2be 100644
--- a/tests/hol4/misc-external/external_OpaqueScript.sml
+++ b/tests/hol4/misc-external/external_OpaqueScript.sml
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
 open primitivesLib divDefLib
 open external_TypesTheory
 
diff --git a/tests/lean/BetreeMain/ExternalFuns.lean b/tests/lean/BetreeMain/ExternalFuns.lean
deleted file mode 100644
index 59beb514..00000000
--- a/tests/lean/BetreeMain/ExternalFuns.lean
+++ /dev/null
@@ -1,9 +0,0 @@
-import Base
-import BetreeMain.Types
-import BetreeMain.Opaque
-
-namespace BetreeMain
-
-def opaque_defs : OpaqueDefs := by sorry
-
-end BetreeMain
diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
index 2eb7fa1f..78e14146 100644
--- a/tests/lean/BetreeMain/Funs.lean
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -2,59 +2,57 @@
 -- [betree_main]: function definitions
 import Base
 import BetreeMain.Types
-import BetreeMain.ExternalFuns
+import BetreeMain.FunsExternal
 open Primitives
-
-namespace BetreeMain
+namespace betree_main
 
 /- [betree_main::betree::load_internal_node] -/
-def betree_load_internal_node_fwd
+def betree.load_internal_node_fwd
   (id : U64) (st : State) :
   Result (State × (betree_list_t (U64 × betree_message_t)))
   :=
-  opaque_defs.betree_utils_load_internal_node_fwd id st
+  betree_utils.load_internal_node_fwd id st
 
 /- [betree_main::betree::store_internal_node] -/
-def betree_store_internal_node_fwd
+def betree.store_internal_node_fwd
   (id : U64) (content : betree_list_t (U64 × betree_message_t)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ←
-      opaque_defs.betree_utils_store_internal_node_fwd id content st
+    let (st0, _) ← betree_utils.store_internal_node_fwd id content st
     Result.ret (st0, ())
 
 /- [betree_main::betree::load_leaf_node] -/
-def betree_load_leaf_node_fwd
+def betree.load_leaf_node_fwd
   (id : U64) (st : State) : Result (State × (betree_list_t (U64 × U64))) :=
-  opaque_defs.betree_utils_load_leaf_node_fwd id st
+  betree_utils.load_leaf_node_fwd id st
 
 /- [betree_main::betree::store_leaf_node] -/
-def betree_store_leaf_node_fwd
+def betree.store_leaf_node_fwd
   (id : U64) (content : betree_list_t (U64 × U64)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ← opaque_defs.betree_utils_store_leaf_node_fwd id content st
+    let (st0, _) ← betree_utils.store_leaf_node_fwd id content st
     Result.ret (st0, ())
 
 /- [betree_main::betree::fresh_node_id] -/
-def betree_fresh_node_id_fwd (counter : U64) : Result U64 :=
+def betree.fresh_node_id_fwd (counter : U64) : Result U64 :=
   do
     let _ ← counter + (U64.ofInt 1 (by intlit))
     Result.ret counter
 
 /- [betree_main::betree::fresh_node_id] -/
-def betree_fresh_node_id_back (counter : U64) : Result U64 :=
+def betree.fresh_node_id_back (counter : U64) : Result U64 :=
   counter + (U64.ofInt 1 (by intlit))
 
 /- [betree_main::betree::NodeIdCounter::{0}::new] -/
-def betree_node_id_counter_new_fwd : Result betree_node_id_counter_t :=
+def betree.NodeIdCounter.new_fwd : Result betree_node_id_counter_t :=
   Result.ret
   { betree_node_id_counter_next_node_id := (U64.ofInt 0 (by intlit)) }
 
 /- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/
-def betree_node_id_counter_fresh_id_fwd
+def betree.NodeIdCounter.fresh_id_fwd
   (self : betree_node_id_counter_t) : Result U64 :=
   do
     let _ ← self.betree_node_id_counter_next_node_id +
@@ -62,7 +60,7 @@ def betree_node_id_counter_fresh_id_fwd
     Result.ret self.betree_node_id_counter_next_node_id
 
 /- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/
-def betree_node_id_counter_fresh_id_back
+def betree.NodeIdCounter.fresh_id_back
   (self : betree_node_id_counter_t) : Result betree_node_id_counter_t :=
   do
     let i ← self.betree_node_id_counter_next_node_id +
@@ -75,7 +73,7 @@ def core_num_u64_max_body : Result U64 :=
 def core_num_u64_max_c : U64 := eval_global core_num_u64_max_body (by simp)
 
 /- [betree_main::betree::upsert_update] -/
-def betree_upsert_update_fwd
+def betree.upsert_update_fwd
   (prev : Option U64) (st : betree_upsert_fun_state_t) : Result U64 :=
   match prev with
   | Option.none =>
@@ -96,17 +94,17 @@ def betree_upsert_update_fwd
       else Result.ret (U64.ofInt 0 (by intlit))
 
 /- [betree_main::betree::List::{1}::len] -/
-divergent def betree_list_len_fwd
+divergent def betree.List.len_fwd
   (T : Type) (self : betree_list_t T) : Result U64 :=
   match self with
   | betree_list_t.Cons t tl =>
     do
-      let i ← betree_list_len_fwd T tl
+      let i ← betree.List.len_fwd T tl
       (U64.ofInt 1 (by intlit)) + i
   | betree_list_t.Nil => Result.ret (U64.ofInt 0 (by intlit))
 
 /- [betree_main::betree::List::{1}::split_at] -/
-divergent def betree_list_split_at_fwd
+divergent def betree.List.split_at_fwd
   (T : Type) (self : betree_list_t T) (n : U64) :
   Result ((betree_list_t T) × (betree_list_t T))
   :=
@@ -117,28 +115,28 @@ divergent def betree_list_split_at_fwd
     | betree_list_t.Cons hd tl =>
       do
         let i ← n - (U64.ofInt 1 (by intlit))
-        let p ← betree_list_split_at_fwd T tl i
+        let p ← betree.List.split_at_fwd T tl i
         let (ls0, ls1) := p
         let l := ls0
         Result.ret (betree_list_t.Cons hd l, ls1)
     | betree_list_t.Nil => Result.fail Error.panic
 
 /- [betree_main::betree::List::{1}::push_front] -/
-def betree_list_push_front_fwd_back
+def betree.List.push_front_fwd_back
   (T : Type) (self : betree_list_t T) (x : T) : Result (betree_list_t T) :=
   let tl := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
   let l := tl
   Result.ret (betree_list_t.Cons x l)
 
 /- [betree_main::betree::List::{1}::pop_front] -/
-def betree_list_pop_front_fwd (T : Type) (self : betree_list_t T) : Result T :=
+def betree.List.pop_front_fwd (T : Type) (self : betree_list_t T) : Result T :=
   let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
   match ls with
   | betree_list_t.Cons x tl => Result.ret x
   | betree_list_t.Nil => Result.fail Error.panic
 
 /- [betree_main::betree::List::{1}::pop_front] -/
-def betree_list_pop_front_back
+def betree.List.pop_front_back
   (T : Type) (self : betree_list_t T) : Result (betree_list_t T) :=
   let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
   match ls with
@@ -146,13 +144,13 @@ def betree_list_pop_front_back
   | betree_list_t.Nil => Result.fail Error.panic
 
 /- [betree_main::betree::List::{1}::hd] -/
-def betree_list_hd_fwd (T : Type) (self : betree_list_t T) : Result T :=
+def betree.List.hd_fwd (T : Type) (self : betree_list_t T) : Result T :=
   match self with
   | betree_list_t.Cons hd l => Result.ret hd
   | betree_list_t.Nil => Result.fail Error.panic
 
 /- [betree_main::betree::List::{2}::head_has_key] -/
-def betree_list_head_has_key_fwd
+def betree.List.head_has_key_fwd
   (T : Type) (self : betree_list_t (U64 × T)) (key : U64) : Result Bool :=
   match self with
   | betree_list_t.Cons hd l => let (i, _) := hd
@@ -160,7 +158,7 @@ def betree_list_head_has_key_fwd
   | betree_list_t.Nil => Result.ret false
 
 /- [betree_main::betree::List::{2}::partition_at_pivot] -/
-divergent def betree_list_partition_at_pivot_fwd
+divergent def betree.List.partition_at_pivot_fwd
   (T : Type) (self : betree_list_t (U64 × T)) (pivot : U64) :
   Result ((betree_list_t (U64 × T)) × (betree_list_t (U64 × T)))
   :=
@@ -171,14 +169,14 @@ divergent def betree_list_partition_at_pivot_fwd
     then Result.ret (betree_list_t.Nil, betree_list_t.Cons (i, t) tl)
     else
       do
-        let p ← betree_list_partition_at_pivot_fwd T tl pivot
+        let p ← betree.List.partition_at_pivot_fwd T tl pivot
         let (ls0, ls1) := p
         let l := ls0
         Result.ret (betree_list_t.Cons (i, t) l, ls1)
   | betree_list_t.Nil => Result.ret (betree_list_t.Nil, betree_list_t.Nil)
 
 /- [betree_main::betree::Leaf::{3}::split] -/
-def betree_leaf_split_fwd
+def betree.Leaf.split_fwd
   (self : betree_leaf_t) (content : betree_list_t (U64 × U64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
   (st : State) :
@@ -186,16 +184,16 @@ def betree_leaf_split_fwd
   :=
   do
     let p ←
-      betree_list_split_at_fwd (U64 × U64) content
+      betree.List.split_at_fwd (U64 × U64) content
         params.betree_params_split_size
     let (content0, content1) := p
-    let p0 ← betree_list_hd_fwd (U64 × U64) content1
+    let p0 ← betree.List.hd_fwd (U64 × U64) content1
     let (pivot, _) := p0
-    let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt
-    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
-    let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0
-    let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st
-    let (st1, _) ← betree_store_leaf_node_fwd id1 content1 st0
+    let id0 ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt
+    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+    let id1 ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt0
+    let (st0, _) ← betree.store_leaf_node_fwd id0 content0 st
+    let (st1, _) ← betree.store_leaf_node_fwd id1 content1 st0
     let n := betree_node_t.Leaf
       {
         betree_leaf_id := id0,
@@ -209,7 +207,7 @@ def betree_leaf_split_fwd
     Result.ret (st1, betree_internal_t.mk self.betree_leaf_id pivot n n0)
 
 /- [betree_main::betree::Leaf::{3}::split] -/
-def betree_leaf_split_back
+def betree.Leaf.split_back
   (self : betree_leaf_t) (content : betree_list_t (U64 × U64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
   (st : State) :
@@ -217,19 +215,19 @@ def betree_leaf_split_back
   :=
   do
     let p ←
-      betree_list_split_at_fwd (U64 × U64) content
+      betree.List.split_at_fwd (U64 × U64) content
         params.betree_params_split_size
     let (content0, content1) := p
-    let _ ← betree_list_hd_fwd (U64 × U64) content1
-    let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt
-    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
-    let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0
-    let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st
-    let _ ← betree_store_leaf_node_fwd id1 content1 st0
-    betree_node_id_counter_fresh_id_back node_id_cnt0
+    let _ ← betree.List.hd_fwd (U64 × U64) content1
+    let id0 ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt
+    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+    let id1 ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt0
+    let (st0, _) ← betree.store_leaf_node_fwd id0 content0 st
+    let _ ← betree.store_leaf_node_fwd id1 content1 st0
+    betree.NodeIdCounter.fresh_id_back node_id_cnt0
 
 /- [betree_main::betree::Node::{5}::lookup_in_bindings] -/
-divergent def betree_node_lookup_in_bindings_fwd
+divergent def betree.Node.lookup_in_bindings_fwd
   (key : U64) (bindings : betree_list_t (U64 × U64)) : Result (Option U64) :=
   match bindings with
   | betree_list_t.Cons hd tl =>
@@ -239,11 +237,11 @@ divergent def betree_node_lookup_in_bindings_fwd
     else
       if i > key
       then Result.ret Option.none
-      else betree_node_lookup_in_bindings_fwd key tl
+      else betree.Node.lookup_in_bindings_fwd key tl
   | betree_list_t.Nil => Result.ret Option.none
 
 /- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/
-divergent def betree_node_lookup_first_message_for_key_fwd
+divergent def betree.Node.lookup_first_message_for_key_fwd
   (key : U64) (msgs : betree_list_t (U64 × betree_message_t)) :
   Result (betree_list_t (U64 × betree_message_t))
   :=
@@ -252,11 +250,11 @@ divergent def betree_node_lookup_first_message_for_key_fwd
     let (i, m) := x
     if i >= key
     then Result.ret (betree_list_t.Cons (i, m) next_msgs)
-    else betree_node_lookup_first_message_for_key_fwd key next_msgs
+    else betree.Node.lookup_first_message_for_key_fwd key next_msgs
   | betree_list_t.Nil => Result.ret betree_list_t.Nil
 
 /- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/
-divergent def betree_node_lookup_first_message_for_key_back
+divergent def betree.Node.lookup_first_message_for_key_back
   (key : U64) (msgs : betree_list_t (U64 × betree_message_t))
   (ret0 : betree_list_t (U64 × betree_message_t)) :
   Result (betree_list_t (U64 × betree_message_t))
@@ -269,70 +267,70 @@ divergent def betree_node_lookup_first_message_for_key_back
     else
       do
         let next_msgs0 ←
-          betree_node_lookup_first_message_for_key_back key next_msgs ret0
+          betree.Node.lookup_first_message_for_key_back key next_msgs ret0
         Result.ret (betree_list_t.Cons (i, m) next_msgs0)
   | betree_list_t.Nil => Result.ret ret0
 
 /- [betree_main::betree::Node::{5}::apply_upserts] -/
-divergent def betree_node_apply_upserts_fwd
+divergent def betree.Node.apply_upserts_fwd
   (msgs : betree_list_t (U64 × betree_message_t)) (prev : Option U64)
   (key : U64) (st : State) :
   Result (State × U64)
   :=
   do
-    let b ← betree_list_head_has_key_fwd betree_message_t msgs key
+    let b ← betree.List.head_has_key_fwd betree_message_t msgs key
     if b
     then
       do
-        let msg ← betree_list_pop_front_fwd (U64 × betree_message_t) msgs
+        let msg ← betree.List.pop_front_fwd (U64 × betree_message_t) msgs
         let (_, m) := msg
         match m with
         | betree_message_t.Insert i => Result.fail Error.panic
         | betree_message_t.Delete => Result.fail Error.panic
         | betree_message_t.Upsert s =>
           do
-            let v ← betree_upsert_update_fwd prev s
+            let v ← betree.upsert_update_fwd prev s
             let msgs0 ←
-              betree_list_pop_front_back (U64 × betree_message_t) msgs
-            betree_node_apply_upserts_fwd msgs0 (Option.some v) key st
+              betree.List.pop_front_back (U64 × betree_message_t) msgs
+            betree.Node.apply_upserts_fwd msgs0 (Option.some v) key st
     else
       do
-        let (st0, v) ← opaque_defs.core_option_option_unwrap_fwd U64 prev st
+        let (st0, v) ← core.option.Option.unwrap_fwd U64 prev st
         let _ ←
-          betree_list_push_front_fwd_back (U64 × betree_message_t) msgs (key,
+          betree.List.push_front_fwd_back (U64 × betree_message_t) msgs (key,
             betree_message_t.Insert v)
         Result.ret (st0, v)
 
 /- [betree_main::betree::Node::{5}::apply_upserts] -/
-divergent def betree_node_apply_upserts_back
+divergent def betree.Node.apply_upserts_back
   (msgs : betree_list_t (U64 × betree_message_t)) (prev : Option U64)
   (key : U64) (st : State) :
   Result (betree_list_t (U64 × betree_message_t))
   :=
   do
-    let b ← betree_list_head_has_key_fwd betree_message_t msgs key
+    let b ← betree.List.head_has_key_fwd betree_message_t msgs key
     if b
     then
       do
-        let msg ← betree_list_pop_front_fwd (U64 × betree_message_t) msgs
+        let msg ← betree.List.pop_front_fwd (U64 × betree_message_t) msgs
         let (_, m) := msg
         match m with
         | betree_message_t.Insert i => Result.fail Error.panic
         | betree_message_t.Delete => Result.fail Error.panic
         | betree_message_t.Upsert s =>
           do
-            let v ← betree_upsert_update_fwd prev s
+            let v ← betree.upsert_update_fwd prev s
             let msgs0 ←
-              betree_list_pop_front_back (U64 × betree_message_t) msgs
-            betree_node_apply_upserts_back msgs0 (Option.some v) key st
+              betree.List.pop_front_back (U64 × betree_message_t) msgs
+            betree.Node.apply_upserts_back msgs0 (Option.some v) key st
     else
       do
-        let (_, v) ← opaque_defs.core_option_option_unwrap_fwd U64 prev st
-        betree_list_push_front_fwd_back (U64 × betree_message_t) msgs (key,
+        let (_, v) ← core.option.Option.unwrap_fwd U64 prev st
+        betree.List.push_front_fwd_back (U64 × betree_message_t) msgs (key,
           betree_message_t.Insert v)
 
 /- [betree_main::betree::Node::{5}::lookup] -/
-mutual divergent def betree_node_lookup_fwd
+mutual divergent def betree.Node.lookup_fwd
   (self : betree_node_t) (key : U64) (st : State) :
   Result (State × (Option U64))
   :=
@@ -340,8 +338,8 @@ mutual divergent def betree_node_lookup_fwd
   | betree_node_t.Internal node =>
     do
       let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, msgs) ← betree_load_internal_node_fwd i st
-      let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
+      let (st0, msgs) ← betree.load_internal_node_fwd i st
+      let pending ← betree.Node.lookup_first_message_for_key_fwd key msgs
       match pending with
       | betree_list_t.Cons p l =>
         let (k, msg) := p
@@ -349,10 +347,10 @@ mutual divergent def betree_node_lookup_fwd
         then
           do
             let (st1, opt) ←
-              betree_internal_lookup_in_children_fwd (betree_internal_t.mk i i0
+              betree.Internal.lookup_in_children_fwd (betree_internal_t.mk i i0
                 n n0) key st0
             let _ ←
-              betree_node_lookup_first_message_for_key_back key msgs
+              betree.Node.lookup_first_message_for_key_back key msgs
                 (betree_list_t.Cons (k, msg) l)
             Result.ret (st1, opt)
         else
@@ -360,58 +358,58 @@ mutual divergent def betree_node_lookup_fwd
           | betree_message_t.Insert v =>
             do
               let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
+                betree.Node.lookup_first_message_for_key_back key msgs
                   (betree_list_t.Cons (k, betree_message_t.Insert v) l)
               Result.ret (st0, Option.some v)
           | betree_message_t.Delete =>
             do
               let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
+                betree.Node.lookup_first_message_for_key_back key msgs
                   (betree_list_t.Cons (k, betree_message_t.Delete) l)
               Result.ret (st0, Option.none)
           | betree_message_t.Upsert ufs =>
             do
               let (st1, v) ←
-                betree_internal_lookup_in_children_fwd (betree_internal_t.mk i
+                betree.Internal.lookup_in_children_fwd (betree_internal_t.mk i
                   i0 n n0) key st0
               let (st2, v0) ←
-                betree_node_apply_upserts_fwd (betree_list_t.Cons (k,
+                betree.Node.apply_upserts_fwd (betree_list_t.Cons (k,
                   betree_message_t.Upsert ufs) l) v key st1
               let node0 ←
-                betree_internal_lookup_in_children_back (betree_internal_t.mk i
+                betree.Internal.lookup_in_children_back (betree_internal_t.mk i
                   i0 n n0) key st0
               let ⟨ i1, _, _, _ ⟩ := node0
               let pending0 ←
-                betree_node_apply_upserts_back (betree_list_t.Cons (k,
+                betree.Node.apply_upserts_back (betree_list_t.Cons (k,
                   betree_message_t.Upsert ufs) l) v key st1
               let msgs0 ←
-                betree_node_lookup_first_message_for_key_back key msgs pending0
-              let (st3, _) ← betree_store_internal_node_fwd i1 msgs0 st2
+                betree.Node.lookup_first_message_for_key_back key msgs pending0
+              let (st3, _) ← betree.store_internal_node_fwd i1 msgs0 st2
               Result.ret (st3, Option.some v0)
       | betree_list_t.Nil =>
         do
           let (st1, opt) ←
-            betree_internal_lookup_in_children_fwd (betree_internal_t.mk i i0 n
+            betree.Internal.lookup_in_children_fwd (betree_internal_t.mk i i0 n
               n0) key st0
           let _ ←
-            betree_node_lookup_first_message_for_key_back key msgs
+            betree.Node.lookup_first_message_for_key_back key msgs
               betree_list_t.Nil
           Result.ret (st1, opt)
   | betree_node_t.Leaf node =>
     do
-      let (st0, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let opt ← betree_node_lookup_in_bindings_fwd key bindings
+      let (st0, bindings) ← betree.load_leaf_node_fwd node.betree_leaf_id st
+      let opt ← betree.Node.lookup_in_bindings_fwd key bindings
       Result.ret (st0, opt)
 
 /- [betree_main::betree::Node::{5}::lookup] -/
-divergent def betree_node_lookup_back
+divergent def betree.Node.lookup_back
   (self : betree_node_t) (key : U64) (st : State) : Result betree_node_t :=
   match self with
   | betree_node_t.Internal node =>
     do
       let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, msgs) ← betree_load_internal_node_fwd i st
-      let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
+      let (st0, msgs) ← betree.load_internal_node_fwd i st
+      let pending ← betree.Node.lookup_first_message_for_key_fwd key msgs
       match pending with
       | betree_list_t.Cons p l =>
         let (k, msg) := p
@@ -419,10 +417,10 @@ divergent def betree_node_lookup_back
         then
           do
             let _ ←
-              betree_node_lookup_first_message_for_key_back key msgs
+              betree.Node.lookup_first_message_for_key_back key msgs
                 (betree_list_t.Cons (k, msg) l)
             let node0 ←
-              betree_internal_lookup_in_children_back (betree_internal_t.mk i
+              betree.Internal.lookup_in_children_back (betree_internal_t.mk i
                 i0 n n0) key st0
             Result.ret (betree_node_t.Internal node0)
         else
@@ -430,64 +428,64 @@ divergent def betree_node_lookup_back
           | betree_message_t.Insert v =>
             do
               let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
+                betree.Node.lookup_first_message_for_key_back key msgs
                   (betree_list_t.Cons (k, betree_message_t.Insert v) l)
               Result.ret (betree_node_t.Internal (betree_internal_t.mk i i0 n
                 n0))
           | betree_message_t.Delete =>
             do
               let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
+                betree.Node.lookup_first_message_for_key_back key msgs
                   (betree_list_t.Cons (k, betree_message_t.Delete) l)
               Result.ret (betree_node_t.Internal (betree_internal_t.mk i i0 n
                 n0))
           | betree_message_t.Upsert ufs =>
             do
               let (st1, v) ←
-                betree_internal_lookup_in_children_fwd (betree_internal_t.mk i
+                betree.Internal.lookup_in_children_fwd (betree_internal_t.mk i
                   i0 n n0) key st0
               let (st2, _) ←
-                betree_node_apply_upserts_fwd (betree_list_t.Cons (k,
+                betree.Node.apply_upserts_fwd (betree_list_t.Cons (k,
                   betree_message_t.Upsert ufs) l) v key st1
               let node0 ←
-                betree_internal_lookup_in_children_back (betree_internal_t.mk i
+                betree.Internal.lookup_in_children_back (betree_internal_t.mk i
                   i0 n n0) key st0
               let ⟨ i1, i2, n1, n2 ⟩ := node0
               let pending0 ←
-                betree_node_apply_upserts_back (betree_list_t.Cons (k,
+                betree.Node.apply_upserts_back (betree_list_t.Cons (k,
                   betree_message_t.Upsert ufs) l) v key st1
               let msgs0 ←
-                betree_node_lookup_first_message_for_key_back key msgs pending0
-              let _ ← betree_store_internal_node_fwd i1 msgs0 st2
+                betree.Node.lookup_first_message_for_key_back key msgs pending0
+              let _ ← betree.store_internal_node_fwd i1 msgs0 st2
               Result.ret (betree_node_t.Internal (betree_internal_t.mk i1 i2 n1
                 n2))
       | betree_list_t.Nil =>
         do
           let _ ←
-            betree_node_lookup_first_message_for_key_back key msgs
+            betree.Node.lookup_first_message_for_key_back key msgs
               betree_list_t.Nil
           let node0 ←
-            betree_internal_lookup_in_children_back (betree_internal_t.mk i i0
+            betree.Internal.lookup_in_children_back (betree_internal_t.mk i i0
               n n0) key st0
           Result.ret (betree_node_t.Internal node0)
   | betree_node_t.Leaf node =>
     do
-      let (_, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let _ ← betree_node_lookup_in_bindings_fwd key bindings
+      let (_, bindings) ← betree.load_leaf_node_fwd node.betree_leaf_id st
+      let _ ← betree.Node.lookup_in_bindings_fwd key bindings
       Result.ret (betree_node_t.Leaf node)
 
 /- [betree_main::betree::Internal::{4}::lookup_in_children] -/
-divergent def betree_internal_lookup_in_children_fwd
+divergent def betree.Internal.lookup_in_children_fwd
   (self : betree_internal_t) (key : U64) (st : State) :
   Result (State × (Option U64))
   :=
   let ⟨ _, i, n, n0 ⟩ := self
   if key < i
-  then betree_node_lookup_fwd n key st
-  else betree_node_lookup_fwd n0 key st
+  then betree.Node.lookup_fwd n key st
+  else betree.Node.lookup_fwd n0 key st
 
 /- [betree_main::betree::Internal::{4}::lookup_in_children] -/
-divergent def betree_internal_lookup_in_children_back
+divergent def betree.Internal.lookup_in_children_back
   (self : betree_internal_t) (key : U64) (st : State) :
   Result betree_internal_t
   :=
@@ -495,17 +493,17 @@ divergent def betree_internal_lookup_in_children_back
   if key < i0
   then
     do
-      let n1 ← betree_node_lookup_back n key st
+      let n1 ← betree.Node.lookup_back n key st
       Result.ret (betree_internal_t.mk i i0 n1 n0)
   else
     do
-      let n1 ← betree_node_lookup_back n0 key st
+      let n1 ← betree.Node.lookup_back n0 key st
       Result.ret (betree_internal_t.mk i i0 n n1)
 
 end
 
 /- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
-divergent def betree_node_lookup_mut_in_bindings_fwd
+divergent def betree.Node.lookup_mut_in_bindings_fwd
   (key : U64) (bindings : betree_list_t (U64 × U64)) :
   Result (betree_list_t (U64 × U64))
   :=
@@ -514,11 +512,11 @@ divergent def betree_node_lookup_mut_in_bindings_fwd
     let (i, i0) := hd
     if i >= key
     then Result.ret (betree_list_t.Cons (i, i0) tl)
-    else betree_node_lookup_mut_in_bindings_fwd key tl
+    else betree.Node.lookup_mut_in_bindings_fwd key tl
   | betree_list_t.Nil => Result.ret betree_list_t.Nil
 
 /- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
-divergent def betree_node_lookup_mut_in_bindings_back
+divergent def betree.Node.lookup_mut_in_bindings_back
   (key : U64) (bindings : betree_list_t (U64 × U64))
   (ret0 : betree_list_t (U64 × U64)) :
   Result (betree_list_t (U64 × U64))
@@ -530,60 +528,60 @@ divergent def betree_node_lookup_mut_in_bindings_back
     then Result.ret ret0
     else
       do
-        let tl0 ← betree_node_lookup_mut_in_bindings_back key tl ret0
+        let tl0 ← betree.Node.lookup_mut_in_bindings_back key tl ret0
         Result.ret (betree_list_t.Cons (i, i0) tl0)
   | betree_list_t.Nil => Result.ret ret0
 
 /- [betree_main::betree::Node::{5}::apply_to_leaf] -/
-def betree_node_apply_to_leaf_fwd_back
+def betree.Node.apply_to_leaf_fwd_back
   (bindings : betree_list_t (U64 × U64)) (key : U64)
   (new_msg : betree_message_t) :
   Result (betree_list_t (U64 × U64))
   :=
   do
-    let bindings0 ← betree_node_lookup_mut_in_bindings_fwd key bindings
-    let b ← betree_list_head_has_key_fwd U64 bindings0 key
+    let bindings0 ← betree.Node.lookup_mut_in_bindings_fwd key bindings
+    let b ← betree.List.head_has_key_fwd U64 bindings0 key
     if b
     then
       do
-        let hd ← betree_list_pop_front_fwd (U64 × U64) bindings0
+        let hd ← betree.List.pop_front_fwd (U64 × U64) bindings0
         match new_msg with
         | betree_message_t.Insert v =>
           do
-            let bindings1 ← betree_list_pop_front_back (U64 × U64) bindings0
+            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
             let bindings2 ←
-              betree_list_push_front_fwd_back (U64 × U64) bindings1 (key, v)
-            betree_node_lookup_mut_in_bindings_back key bindings bindings2
+              betree.List.push_front_fwd_back (U64 × U64) bindings1 (key, v)
+            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
         | betree_message_t.Delete =>
           do
-            let bindings1 ← betree_list_pop_front_back (U64 × U64) bindings0
-            betree_node_lookup_mut_in_bindings_back key bindings bindings1
+            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
+            betree.Node.lookup_mut_in_bindings_back key bindings bindings1
         | betree_message_t.Upsert s =>
           do
             let (_, i) := hd
-            let v ← betree_upsert_update_fwd (Option.some i) s
-            let bindings1 ← betree_list_pop_front_back (U64 × U64) bindings0
+            let v ← betree.upsert_update_fwd (Option.some i) s
+            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
             let bindings2 ←
-              betree_list_push_front_fwd_back (U64 × U64) bindings1 (key, v)
-            betree_node_lookup_mut_in_bindings_back key bindings bindings2
+              betree.List.push_front_fwd_back (U64 × U64) bindings1 (key, v)
+            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
     else
       match new_msg with
       | betree_message_t.Insert v =>
         do
           let bindings1 ←
-            betree_list_push_front_fwd_back (U64 × U64) bindings0 (key, v)
-          betree_node_lookup_mut_in_bindings_back key bindings bindings1
+            betree.List.push_front_fwd_back (U64 × U64) bindings0 (key, v)
+          betree.Node.lookup_mut_in_bindings_back key bindings bindings1
       | betree_message_t.Delete =>
-        betree_node_lookup_mut_in_bindings_back key bindings bindings0
+        betree.Node.lookup_mut_in_bindings_back key bindings bindings0
       | betree_message_t.Upsert s =>
         do
-          let v ← betree_upsert_update_fwd Option.none s
+          let v ← betree.upsert_update_fwd Option.none s
           let bindings1 ←
-            betree_list_push_front_fwd_back (U64 × U64) bindings0 (key, v)
-          betree_node_lookup_mut_in_bindings_back key bindings bindings1
+            betree.List.push_front_fwd_back (U64 × U64) bindings0 (key, v)
+          betree.Node.lookup_mut_in_bindings_back key bindings bindings1
 
 /- [betree_main::betree::Node::{5}::apply_messages_to_leaf] -/
-divergent def betree_node_apply_messages_to_leaf_fwd_back
+divergent def betree.Node.apply_messages_to_leaf_fwd_back
   (bindings : betree_list_t (U64 × U64))
   (new_msgs : betree_list_t (U64 × betree_message_t)) :
   Result (betree_list_t (U64 × U64))
@@ -592,12 +590,12 @@ divergent def betree_node_apply_messages_to_leaf_fwd_back
   | betree_list_t.Cons new_msg new_msgs_tl =>
     do
       let (i, m) := new_msg
-      let bindings0 ← betree_node_apply_to_leaf_fwd_back bindings i m
-      betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
+      let bindings0 ← betree.Node.apply_to_leaf_fwd_back bindings i m
+      betree.Node.apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
   | betree_list_t.Nil => Result.ret bindings
 
 /- [betree_main::betree::Node::{5}::filter_messages_for_key] -/
-divergent def betree_node_filter_messages_for_key_fwd_back
+divergent def betree.Node.filter_messages_for_key_fwd_back
   (key : U64) (msgs : betree_list_t (U64 × betree_message_t)) :
   Result (betree_list_t (U64 × betree_message_t))
   :=
@@ -608,14 +606,14 @@ divergent def betree_node_filter_messages_for_key_fwd_back
     then
       do
         let msgs0 ←
-          betree_list_pop_front_back (U64 × betree_message_t)
+          betree.List.pop_front_back (U64 × betree_message_t)
             (betree_list_t.Cons (k, m) l)
-        betree_node_filter_messages_for_key_fwd_back key msgs0
+        betree.Node.filter_messages_for_key_fwd_back key msgs0
     else Result.ret (betree_list_t.Cons (k, m) l)
   | betree_list_t.Nil => Result.ret betree_list_t.Nil
 
 /- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
-divergent def betree_node_lookup_first_message_after_key_fwd
+divergent def betree.Node.lookup_first_message_after_key_fwd
   (key : U64) (msgs : betree_list_t (U64 × betree_message_t)) :
   Result (betree_list_t (U64 × betree_message_t))
   :=
@@ -623,12 +621,12 @@ divergent def betree_node_lookup_first_message_after_key_fwd
   | betree_list_t.Cons p next_msgs =>
     let (k, m) := p
     if k = key
-    then betree_node_lookup_first_message_after_key_fwd key next_msgs
+    then betree.Node.lookup_first_message_after_key_fwd key next_msgs
     else Result.ret (betree_list_t.Cons (k, m) next_msgs)
   | betree_list_t.Nil => Result.ret betree_list_t.Nil
 
 /- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
-divergent def betree_node_lookup_first_message_after_key_back
+divergent def betree.Node.lookup_first_message_after_key_back
   (key : U64) (msgs : betree_list_t (U64 × betree_message_t))
   (ret0 : betree_list_t (U64 × betree_message_t)) :
   Result (betree_list_t (U64 × betree_message_t))
@@ -640,79 +638,79 @@ divergent def betree_node_lookup_first_message_after_key_back
     then
       do
         let next_msgs0 ←
-          betree_node_lookup_first_message_after_key_back key next_msgs ret0
+          betree.Node.lookup_first_message_after_key_back key next_msgs ret0
         Result.ret (betree_list_t.Cons (k, m) next_msgs0)
     else Result.ret ret0
   | betree_list_t.Nil => Result.ret ret0
 
 /- [betree_main::betree::Node::{5}::apply_to_internal] -/
-def betree_node_apply_to_internal_fwd_back
+def betree.Node.apply_to_internal_fwd_back
   (msgs : betree_list_t (U64 × betree_message_t)) (key : U64)
   (new_msg : betree_message_t) :
   Result (betree_list_t (U64 × betree_message_t))
   :=
   do
-    let msgs0 ← betree_node_lookup_first_message_for_key_fwd key msgs
-    let b ← betree_list_head_has_key_fwd betree_message_t msgs0 key
+    let msgs0 ← betree.Node.lookup_first_message_for_key_fwd key msgs
+    let b ← betree.List.head_has_key_fwd betree_message_t msgs0 key
     if b
     then
       match new_msg with
       | betree_message_t.Insert i =>
         do
-          let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0
+          let msgs1 ← betree.Node.filter_messages_for_key_fwd_back key msgs0
           let msgs2 ←
-            betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+            betree.List.push_front_fwd_back (U64 × betree_message_t) msgs1
               (key, betree_message_t.Insert i)
-          betree_node_lookup_first_message_for_key_back key msgs msgs2
+          betree.Node.lookup_first_message_for_key_back key msgs msgs2
       | betree_message_t.Delete =>
         do
-          let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0
+          let msgs1 ← betree.Node.filter_messages_for_key_fwd_back key msgs0
           let msgs2 ←
-            betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+            betree.List.push_front_fwd_back (U64 × betree_message_t) msgs1
               (key, betree_message_t.Delete)
-          betree_node_lookup_first_message_for_key_back key msgs msgs2
+          betree.Node.lookup_first_message_for_key_back key msgs msgs2
       | betree_message_t.Upsert s =>
         do
-          let p ← betree_list_hd_fwd (U64 × betree_message_t) msgs0
+          let p ← betree.List.hd_fwd (U64 × betree_message_t) msgs0
           let (_, m) := p
           match m with
           | betree_message_t.Insert prev =>
             do
-              let v ← betree_upsert_update_fwd (Option.some prev) s
+              let v ← betree.upsert_update_fwd (Option.some prev) s
               let msgs1 ←
-                betree_list_pop_front_back (U64 × betree_message_t) msgs0
+                betree.List.pop_front_back (U64 × betree_message_t) msgs0
               let msgs2 ←
-                betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+                betree.List.push_front_fwd_back (U64 × betree_message_t) msgs1
                   (key, betree_message_t.Insert v)
-              betree_node_lookup_first_message_for_key_back key msgs msgs2
+              betree.Node.lookup_first_message_for_key_back key msgs msgs2
           | betree_message_t.Delete =>
             do
-              let v ← betree_upsert_update_fwd Option.none s
+              let v ← betree.upsert_update_fwd Option.none s
               let msgs1 ←
-                betree_list_pop_front_back (U64 × betree_message_t) msgs0
+                betree.List.pop_front_back (U64 × betree_message_t) msgs0
               let msgs2 ←
-                betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+                betree.List.push_front_fwd_back (U64 × betree_message_t) msgs1
                   (key, betree_message_t.Insert v)
-              betree_node_lookup_first_message_for_key_back key msgs msgs2
+              betree.Node.lookup_first_message_for_key_back key msgs msgs2
           | betree_message_t.Upsert ufs =>
             do
               let msgs1 ←
-                betree_node_lookup_first_message_after_key_fwd key msgs0
+                betree.Node.lookup_first_message_after_key_fwd key msgs0
               let msgs2 ←
-                betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+                betree.List.push_front_fwd_back (U64 × betree_message_t) msgs1
                   (key, betree_message_t.Upsert s)
               let msgs3 ←
-                betree_node_lookup_first_message_after_key_back key msgs0 msgs2
-              betree_node_lookup_first_message_for_key_back key msgs msgs3
+                betree.Node.lookup_first_message_after_key_back key msgs0 msgs2
+              betree.Node.lookup_first_message_for_key_back key msgs msgs3
     else
       do
         let msgs1 ←
-          betree_list_push_front_fwd_back (U64 × betree_message_t) msgs0 (key,
+          betree.List.push_front_fwd_back (U64 × betree_message_t) msgs0 (key,
             new_msg)
-        betree_node_lookup_first_message_for_key_back key msgs msgs1
+        betree.Node.lookup_first_message_for_key_back key msgs msgs1
 
 /- [betree_main::betree::Node::{5}::apply_messages_to_internal] -/
-divergent def betree_node_apply_messages_to_internal_fwd_back
+divergent def betree.Node.apply_messages_to_internal_fwd_back
   (msgs : betree_list_t (U64 × betree_message_t))
   (new_msgs : betree_list_t (U64 × betree_message_t)) :
   Result (betree_list_t (U64 × betree_message_t))
@@ -721,12 +719,12 @@ divergent def betree_node_apply_messages_to_internal_fwd_back
   | betree_list_t.Cons new_msg new_msgs_tl =>
     do
       let (i, m) := new_msg
-      let msgs0 ← betree_node_apply_to_internal_fwd_back msgs i m
-      betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl
+      let msgs0 ← betree.Node.apply_to_internal_fwd_back msgs i m
+      betree.Node.apply_messages_to_internal_fwd_back msgs0 new_msgs_tl
   | betree_list_t.Nil => Result.ret msgs
 
 /- [betree_main::betree::Node::{5}::apply_messages] -/
-mutual divergent def betree_node_apply_messages_fwd
+mutual divergent def betree.Node.apply_messages_fwd
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
   (msgs : betree_list_t (U64 × betree_message_t)) (st : State) :
@@ -736,49 +734,49 @@ mutual divergent def betree_node_apply_messages_fwd
   | betree_node_t.Internal node =>
     do
       let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, content) ← betree_load_internal_node_fwd i st
+      let (st0, content) ← betree.load_internal_node_fwd i st
       let content0 ←
-        betree_node_apply_messages_to_internal_fwd_back content msgs
-      let num_msgs ← betree_list_len_fwd (U64 × betree_message_t) content0
+        betree.Node.apply_messages_to_internal_fwd_back content msgs
+      let num_msgs ← betree.List.len_fwd (U64 × betree_message_t) content0
       if num_msgs >= params.betree_params_min_flush_size
       then
         do
           let (st1, content1) ←
-            betree_internal_flush_fwd (betree_internal_t.mk i i0 n n0) params
+            betree.Internal.flush_fwd (betree_internal_t.mk i i0 n n0) params
               node_id_cnt content0 st0
           let (node0, _) ←
-            betree_internal_flush_back (betree_internal_t.mk i i0 n n0) params
+            betree.Internal.flush_back (betree_internal_t.mk i i0 n n0) params
               node_id_cnt content0 st0
           let ⟨ i1, _, _, _ ⟩ := node0
-          let (st2, _) ← betree_store_internal_node_fwd i1 content1 st1
+          let (st2, _) ← betree.store_internal_node_fwd i1 content1 st1
           Result.ret (st2, ())
       else
         do
-          let (st1, _) ← betree_store_internal_node_fwd i content0 st0
+          let (st1, _) ← betree.store_internal_node_fwd i content0 st0
           Result.ret (st1, ())
   | betree_node_t.Leaf node =>
     do
-      let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs
-      let len ← betree_list_len_fwd (U64 × U64) content0
+      let (st0, content) ← betree.load_leaf_node_fwd node.betree_leaf_id st
+      let content0 ← betree.Node.apply_messages_to_leaf_fwd_back content msgs
+      let len ← betree.List.len_fwd (U64 × U64) content0
       let i ← (U64.ofInt 2 (by intlit)) * params.betree_params_split_size
       if len >= i
       then
         do
           let (st1, _) ←
-            betree_leaf_split_fwd node content0 params node_id_cnt st0
+            betree.Leaf.split_fwd node content0 params node_id_cnt st0
           let (st2, _) ←
-            betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
+            betree.store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
               st1
           Result.ret (st2, ())
       else
         do
           let (st1, _) ←
-            betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
+            betree.store_leaf_node_fwd node.betree_leaf_id content0 st0
           Result.ret (st1, ())
 
 /- [betree_main::betree::Node::{5}::apply_messages] -/
-divergent def betree_node_apply_messages_back
+divergent def betree.Node.apply_messages_back
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
   (msgs : betree_list_t (U64 × betree_message_t)) (st : State) :
@@ -788,53 +786,53 @@ divergent def betree_node_apply_messages_back
   | betree_node_t.Internal node =>
     do
       let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, content) ← betree_load_internal_node_fwd i st
+      let (st0, content) ← betree.load_internal_node_fwd i st
       let content0 ←
-        betree_node_apply_messages_to_internal_fwd_back content msgs
-      let num_msgs ← betree_list_len_fwd (U64 × betree_message_t) content0
+        betree.Node.apply_messages_to_internal_fwd_back content msgs
+      let num_msgs ← betree.List.len_fwd (U64 × betree_message_t) content0
       if num_msgs >= params.betree_params_min_flush_size
       then
         do
           let (st1, content1) ←
-            betree_internal_flush_fwd (betree_internal_t.mk i i0 n n0) params
+            betree.Internal.flush_fwd (betree_internal_t.mk i i0 n n0) params
               node_id_cnt content0 st0
           let (node0, node_id_cnt0) ←
-            betree_internal_flush_back (betree_internal_t.mk i i0 n n0) params
+            betree.Internal.flush_back (betree_internal_t.mk i i0 n n0) params
               node_id_cnt content0 st0
           let ⟨ i1, i2, n1, n2 ⟩ := node0
-          let _ ← betree_store_internal_node_fwd i1 content1 st1
+          let _ ← betree.store_internal_node_fwd i1 content1 st1
           Result.ret (betree_node_t.Internal (betree_internal_t.mk i1 i2 n1
             n2), node_id_cnt0)
       else
         do
-          let _ ← betree_store_internal_node_fwd i content0 st0
+          let _ ← betree.store_internal_node_fwd i content0 st0
           Result.ret (betree_node_t.Internal (betree_internal_t.mk i i0 n n0),
             node_id_cnt)
   | betree_node_t.Leaf node =>
     do
-      let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs
-      let len ← betree_list_len_fwd (U64 × U64) content0
+      let (st0, content) ← betree.load_leaf_node_fwd node.betree_leaf_id st
+      let content0 ← betree.Node.apply_messages_to_leaf_fwd_back content msgs
+      let len ← betree.List.len_fwd (U64 × U64) content0
       let i ← (U64.ofInt 2 (by intlit)) * params.betree_params_split_size
       if len >= i
       then
         do
           let (st1, new_node) ←
-            betree_leaf_split_fwd node content0 params node_id_cnt st0
+            betree.Leaf.split_fwd node content0 params node_id_cnt st0
           let _ ←
-            betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
+            betree.store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
               st1
           let node_id_cnt0 ←
-            betree_leaf_split_back node content0 params node_id_cnt st0
+            betree.Leaf.split_back node content0 params node_id_cnt st0
           Result.ret (betree_node_t.Internal new_node, node_id_cnt0)
       else
         do
-          let _ ← betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
+          let _ ← betree.store_leaf_node_fwd node.betree_leaf_id content0 st0
           Result.ret (betree_node_t.Leaf { node with betree_leaf_size := len },
             node_id_cnt)
 
 /- [betree_main::betree::Internal::{4}::flush] -/
-divergent def betree_internal_flush_fwd
+divergent def betree.Internal.flush_fwd
   (self : betree_internal_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
   (content : betree_list_t (U64 × betree_message_t)) (st : State) :
@@ -842,39 +840,39 @@ divergent def betree_internal_flush_fwd
   :=
   do
     let ⟨ _, i, n, n0 ⟩ := self
-    let p ← betree_list_partition_at_pivot_fwd betree_message_t content i
+    let p ← betree.List.partition_at_pivot_fwd betree_message_t content i
     let (msgs_left, msgs_right) := p
-    let len_left ← betree_list_len_fwd (U64 × betree_message_t) msgs_left
+    let len_left ← betree.List.len_fwd (U64 × betree_message_t) msgs_left
     if len_left >= params.betree_params_min_flush_size
     then
       do
         let (st0, _) ←
-          betree_node_apply_messages_fwd n params node_id_cnt msgs_left st
+          betree.Node.apply_messages_fwd n params node_id_cnt msgs_left st
         let (_, node_id_cnt0) ←
-          betree_node_apply_messages_back n params node_id_cnt msgs_left st
+          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
         let len_right ←
-          betree_list_len_fwd (U64 × betree_message_t) msgs_right
+          betree.List.len_fwd (U64 × betree_message_t) msgs_right
         if len_right >= params.betree_params_min_flush_size
         then
           do
             let (st1, _) ←
-              betree_node_apply_messages_fwd n0 params node_id_cnt0 msgs_right
+              betree.Node.apply_messages_fwd n0 params node_id_cnt0 msgs_right
                 st0
             let _ ←
-              betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right
+              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
                 st0
             Result.ret (st1, betree_list_t.Nil)
         else Result.ret (st0, msgs_right)
     else
       do
         let (st0, _) ←
-          betree_node_apply_messages_fwd n0 params node_id_cnt msgs_right st
+          betree.Node.apply_messages_fwd n0 params node_id_cnt msgs_right st
         let _ ←
-          betree_node_apply_messages_back n0 params node_id_cnt msgs_right st
+          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
         Result.ret (st0, msgs_left)
 
 /- [betree_main::betree::Internal::{4}::flush] -/
-divergent def betree_internal_flush_back
+divergent def betree.Internal.flush_back
   (self : betree_internal_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
   (content : betree_list_t (U64 × betree_message_t)) (st : State) :
@@ -882,36 +880,36 @@ divergent def betree_internal_flush_back
   :=
   do
     let ⟨ i, i0, n, n0 ⟩ := self
-    let p ← betree_list_partition_at_pivot_fwd betree_message_t content i0
+    let p ← betree.List.partition_at_pivot_fwd betree_message_t content i0
     let (msgs_left, msgs_right) := p
-    let len_left ← betree_list_len_fwd (U64 × betree_message_t) msgs_left
+    let len_left ← betree.List.len_fwd (U64 × betree_message_t) msgs_left
     if len_left >= params.betree_params_min_flush_size
     then
       do
         let (st0, _) ←
-          betree_node_apply_messages_fwd n params node_id_cnt msgs_left st
+          betree.Node.apply_messages_fwd n params node_id_cnt msgs_left st
         let (n1, node_id_cnt0) ←
-          betree_node_apply_messages_back n params node_id_cnt msgs_left st
+          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
         let len_right ←
-          betree_list_len_fwd (U64 × betree_message_t) msgs_right
+          betree.List.len_fwd (U64 × betree_message_t) msgs_right
         if len_right >= params.betree_params_min_flush_size
         then
           do
             let (n2, node_id_cnt1) ←
-              betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right
+              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
                 st0
             Result.ret (betree_internal_t.mk i i0 n1 n2, node_id_cnt1)
         else Result.ret (betree_internal_t.mk i i0 n1 n0, node_id_cnt0)
     else
       do
         let (n1, node_id_cnt0) ←
-          betree_node_apply_messages_back n0 params node_id_cnt msgs_right st
+          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
         Result.ret (betree_internal_t.mk i i0 n n1, node_id_cnt0)
 
 end
 
 /- [betree_main::betree::Node::{5}::apply] -/
-def betree_node_apply_fwd
+def betree.Node.apply_fwd
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t) (key : U64)
   (new_msg : betree_message_t) (st : State) :
@@ -920,34 +918,34 @@ def betree_node_apply_fwd
   do
     let l := betree_list_t.Nil
     let (st0, _) ←
-      betree_node_apply_messages_fwd self params node_id_cnt
+      betree.Node.apply_messages_fwd self params node_id_cnt
         (betree_list_t.Cons (key, new_msg) l) st
     let _ ←
-      betree_node_apply_messages_back self params node_id_cnt
+      betree.Node.apply_messages_back self params node_id_cnt
         (betree_list_t.Cons (key, new_msg) l) st
     Result.ret (st0, ())
 
 /- [betree_main::betree::Node::{5}::apply] -/
-def betree_node_apply_back
+def betree.Node.apply_back
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t) (key : U64)
   (new_msg : betree_message_t) (st : State) :
   Result (betree_node_t × betree_node_id_counter_t)
   :=
   let l := betree_list_t.Nil
-  betree_node_apply_messages_back self params node_id_cnt (betree_list_t.Cons
+  betree.Node.apply_messages_back self params node_id_cnt (betree_list_t.Cons
     (key, new_msg) l) st
 
 /- [betree_main::betree::BeTree::{6}::new] -/
-def betree_be_tree_new_fwd
+def betree.BeTree.new_fwd
   (min_flush_size : U64) (split_size : U64) (st : State) :
   Result (State × betree_be_tree_t)
   :=
   do
-    let node_id_cnt ← betree_node_id_counter_new_fwd
-    let id ← betree_node_id_counter_fresh_id_fwd node_id_cnt
-    let (st0, _) ← betree_store_leaf_node_fwd id betree_list_t.Nil st
-    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
+    let node_id_cnt ← betree.NodeIdCounter.new_fwd
+    let id ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt
+    let (st0, _) ← betree.store_leaf_node_fwd id betree_list_t.Nil st
+    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
     Result.ret (st0,
       {
         betree_be_tree_params :=
@@ -965,103 +963,103 @@ def betree_be_tree_new_fwd
       })
 
 /- [betree_main::betree::BeTree::{6}::apply] -/
-def betree_be_tree_apply_fwd
+def betree.BeTree.apply_fwd
   (self : betree_be_tree_t) (key : U64) (msg : betree_message_t) (st : State) :
   Result (State × Unit)
   :=
   do
     let (st0, _) ←
-      betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
+      betree.Node.apply_fwd self.betree_be_tree_root self.betree_be_tree_params
         self.betree_be_tree_node_id_cnt key msg st
     let _ ←
-      betree_node_apply_back self.betree_be_tree_root
+      betree.Node.apply_back self.betree_be_tree_root
         self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st
     Result.ret (st0, ())
 
 /- [betree_main::betree::BeTree::{6}::apply] -/
-def betree_be_tree_apply_back
+def betree.BeTree.apply_back
   (self : betree_be_tree_t) (key : U64) (msg : betree_message_t) (st : State) :
   Result betree_be_tree_t
   :=
   do
     let (n, nic) ←
-      betree_node_apply_back self.betree_be_tree_root
+      betree.Node.apply_back self.betree_be_tree_root
         self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st
     Result.ret
       { self with betree_be_tree_node_id_cnt := nic, betree_be_tree_root := n }
 
 /- [betree_main::betree::BeTree::{6}::insert] -/
-def betree_be_tree_insert_fwd
+def betree.BeTree.insert_fwd
   (self : betree_be_tree_t) (key : U64) (value : U64) (st : State) :
   Result (State × Unit)
   :=
   do
     let (st0, _) ←
-      betree_be_tree_apply_fwd self key (betree_message_t.Insert value) st
+      betree.BeTree.apply_fwd self key (betree_message_t.Insert value) st
     let _ ←
-      betree_be_tree_apply_back self key (betree_message_t.Insert value) st
+      betree.BeTree.apply_back self key (betree_message_t.Insert value) st
     Result.ret (st0, ())
 
 /- [betree_main::betree::BeTree::{6}::insert] -/
-def betree_be_tree_insert_back
+def betree.BeTree.insert_back
   (self : betree_be_tree_t) (key : U64) (value : U64) (st : State) :
   Result betree_be_tree_t
   :=
-  betree_be_tree_apply_back self key (betree_message_t.Insert value) st
+  betree.BeTree.apply_back self key (betree_message_t.Insert value) st
 
 /- [betree_main::betree::BeTree::{6}::delete] -/
-def betree_be_tree_delete_fwd
+def betree.BeTree.delete_fwd
   (self : betree_be_tree_t) (key : U64) (st : State) :
   Result (State × Unit)
   :=
   do
     let (st0, _) ←
-      betree_be_tree_apply_fwd self key betree_message_t.Delete st
-    let _ ← betree_be_tree_apply_back self key betree_message_t.Delete st
+      betree.BeTree.apply_fwd self key betree_message_t.Delete st
+    let _ ← betree.BeTree.apply_back self key betree_message_t.Delete st
     Result.ret (st0, ())
 
 /- [betree_main::betree::BeTree::{6}::delete] -/
-def betree_be_tree_delete_back
+def betree.BeTree.delete_back
   (self : betree_be_tree_t) (key : U64) (st : State) :
   Result betree_be_tree_t
   :=
-  betree_be_tree_apply_back self key betree_message_t.Delete st
+  betree.BeTree.apply_back self key betree_message_t.Delete st
 
 /- [betree_main::betree::BeTree::{6}::upsert] -/
-def betree_be_tree_upsert_fwd
+def betree.BeTree.upsert_fwd
   (self : betree_be_tree_t) (key : U64) (upd : betree_upsert_fun_state_t)
   (st : State) :
   Result (State × Unit)
   :=
   do
     let (st0, _) ←
-      betree_be_tree_apply_fwd self key (betree_message_t.Upsert upd) st
+      betree.BeTree.apply_fwd self key (betree_message_t.Upsert upd) st
     let _ ←
-      betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st
+      betree.BeTree.apply_back self key (betree_message_t.Upsert upd) st
     Result.ret (st0, ())
 
 /- [betree_main::betree::BeTree::{6}::upsert] -/
-def betree_be_tree_upsert_back
+def betree.BeTree.upsert_back
   (self : betree_be_tree_t) (key : U64) (upd : betree_upsert_fun_state_t)
   (st : State) :
   Result betree_be_tree_t
   :=
-  betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st
+  betree.BeTree.apply_back self key (betree_message_t.Upsert upd) st
 
 /- [betree_main::betree::BeTree::{6}::lookup] -/
-def betree_be_tree_lookup_fwd
+def betree.BeTree.lookup_fwd
   (self : betree_be_tree_t) (key : U64) (st : State) :
   Result (State × (Option U64))
   :=
-  betree_node_lookup_fwd self.betree_be_tree_root key st
+  betree.Node.lookup_fwd self.betree_be_tree_root key st
 
 /- [betree_main::betree::BeTree::{6}::lookup] -/
-def betree_be_tree_lookup_back
+def betree.BeTree.lookup_back
   (self : betree_be_tree_t) (key : U64) (st : State) :
   Result betree_be_tree_t
   :=
   do
-    let n ← betree_node_lookup_back self.betree_be_tree_root key st
+    let n ← betree.Node.lookup_back self.betree_be_tree_root key st
     Result.ret { self with betree_be_tree_root := n }
 
 /- [betree_main::main] -/
@@ -1071,4 +1069,4 @@ def main_fwd : Result Unit :=
 /- Unit test for [betree_main::main] -/
 #assert (main_fwd == .ret ())
 
-end BetreeMain
+end betree_main
diff --git a/tests/lean/BetreeMain/FunsExternal.lean b/tests/lean/BetreeMain/FunsExternal.lean
new file mode 100644
index 00000000..0c715ef9
--- /dev/null
+++ b/tests/lean/BetreeMain/FunsExternal.lean
@@ -0,0 +1,35 @@
+-- [betree_main]: external functions.
+import Base
+import BetreeMain.Types
+open Primitives
+open betree_main
+
+-- TODO: fill those bodies
+
+/- [betree_main::betree_utils::load_internal_node] -/
+def betree_utils.load_internal_node_fwd
+  :
+  U64 → State → Result (State × (betree_list_t (U64 × betree_message_t))) :=
+  fun _ _ => .fail .panic
+
+/- [betree_main::betree_utils::store_internal_node] -/
+def betree_utils.store_internal_node_fwd
+  :
+  U64 → betree_list_t (U64 × betree_message_t) → State → Result (State
+    × Unit) :=
+  fun _ _ _ => .fail .panic
+
+/- [betree_main::betree_utils::load_leaf_node] -/
+def betree_utils.load_leaf_node_fwd
+  : U64 → State → Result (State × (betree_list_t (U64 × U64))) :=
+  fun _ _ => .fail .panic
+
+/- [betree_main::betree_utils::store_leaf_node] -/
+def betree_utils.store_leaf_node_fwd
+  : U64 → betree_list_t (U64 × U64) → State → Result (State × Unit) :=
+  fun _ _ _ => .fail .panic
+
+/- [core::option::Option::{0}::unwrap] -/
+def core.option.Option.unwrap_fwd
+  (T : Type) : Option T → State → Result (State × T) :=
+  fun _ _ => .fail .panic
diff --git a/tests/lean/BetreeMain/FunsExternal_Template.lean b/tests/lean/BetreeMain/FunsExternal_Template.lean
new file mode 100644
index 00000000..9b5a54e5
--- /dev/null
+++ b/tests/lean/BetreeMain/FunsExternal_Template.lean
@@ -0,0 +1,31 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import BetreeMain.Types
+open Primitives
+open betree_main
+
+/- [betree_main::betree_utils::load_internal_node] -/
+axiom betree_utils.load_internal_node_fwd
+  :
+  U64 → State → Result (State × (betree_list_t (U64 × betree_message_t)))
+
+/- [betree_main::betree_utils::store_internal_node] -/
+axiom betree_utils.store_internal_node_fwd
+  :
+  U64 → betree_list_t (U64 × betree_message_t) → State → Result (State
+    × Unit)
+
+/- [betree_main::betree_utils::load_leaf_node] -/
+axiom betree_utils.load_leaf_node_fwd
+  : U64 → State → Result (State × (betree_list_t (U64 × U64)))
+
+/- [betree_main::betree_utils::store_leaf_node] -/
+axiom betree_utils.store_leaf_node_fwd
+  : U64 → betree_list_t (U64 × U64) → State → Result (State × Unit)
+
+/- [core::option::Option::{0}::unwrap] -/
+axiom core.option.Option.unwrap_fwd
+  (T : Type) : Option T → State → Result (State × T)
+
diff --git a/tests/lean/BetreeMain/Opaque.lean b/tests/lean/BetreeMain/Opaque.lean
deleted file mode 100644
index d043186b..00000000
--- a/tests/lean/BetreeMain/Opaque.lean
+++ /dev/null
@@ -1,35 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [betree_main]: opaque function definitions
-import Base
-import BetreeMain.Types
-open Primitives
-
-namespace BetreeMain
-
-structure OpaqueDefs where
-  
-  /- [betree_main::betree_utils::load_internal_node] -/
-  betree_utils_load_internal_node_fwd
-    :
-    U64 → State → Result (State × (betree_list_t (U64 ×
-      betree_message_t)))
-  
-  /- [betree_main::betree_utils::store_internal_node] -/
-  betree_utils_store_internal_node_fwd
-    :
-    U64 → betree_list_t (U64 × betree_message_t) → State → Result (State
-      × Unit)
-  
-  /- [betree_main::betree_utils::load_leaf_node] -/
-  betree_utils_load_leaf_node_fwd
-    : U64 → State → Result (State × (betree_list_t (U64 × U64)))
-  
-  /- [betree_main::betree_utils::store_leaf_node] -/
-  betree_utils_store_leaf_node_fwd
-    : U64 → betree_list_t (U64 × U64) → State → Result (State × Unit)
-  
-  /- [core::option::Option::{0}::unwrap] -/
-  core_option_option_unwrap_fwd
-    (T : Type) : Option T → State → Result (State × T)
-  
-end BetreeMain
diff --git a/tests/lean/BetreeMain/Types.lean b/tests/lean/BetreeMain/Types.lean
index cfed6a28..3ecbd668 100644
--- a/tests/lean/BetreeMain/Types.lean
+++ b/tests/lean/BetreeMain/Types.lean
@@ -2,8 +2,7 @@
 -- [betree_main]: type definitions
 import Base
 open Primitives
-
-namespace BetreeMain
+namespace betree_main
 
 /- [betree_main::betree::List] -/
 inductive betree_list_t (T : Type) :=
@@ -57,4 +56,4 @@ structure betree_be_tree_t where
 /- The state type used in the state-error monad -/
 axiom State : Type
 
-end BetreeMain
+end betree_main
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
index 9f6a47de..39c270be 100644
--- a/tests/lean/Constants.lean
+++ b/tests/lean/Constants.lean
@@ -2,8 +2,7 @@
 -- [constants]
 import Base
 open Primitives
-
-namespace Constants
+namespace constants
 
 /- [constants::X0] -/
 def x0_body : Result U32 := Result.ret (U32.ofInt 0 (by intlit))
@@ -69,11 +68,11 @@ structure wrap_t (T : Type) where
   wrap_val : T
 
 /- [constants::Wrap::{0}::new] -/
-def wrap_new_fwd (T : Type) (val : T) : Result (wrap_t T) :=
+def Wrap.new_fwd (T : Type) (val : T) : Result (wrap_t T) :=
   Result.ret { wrap_val := val }
 
 /- [constants::Y] -/
-def y_body : Result (wrap_t I32) := wrap_new_fwd I32 (I32.ofInt 2 (by intlit))
+def y_body : Result (wrap_t I32) := Wrap.new_fwd I32 (I32.ofInt 2 (by intlit))
 def y_c : wrap_t I32 := eval_global y_body (by simp)
 
 /- [constants::unwrap_y] -/
@@ -132,4 +131,4 @@ def s4_body : Result (pair_t U32 U32) :=
   mk_pair1_fwd (U32.ofInt 7 (by intlit)) (U32.ofInt 8 (by intlit))
 def s4_c : pair_t U32 U32 := eval_global s4_body (by simp)
 
-end Constants
+end constants
diff --git a/tests/lean/External/ExternalFuns.lean b/tests/lean/External/ExternalFuns.lean
deleted file mode 100644
index d63db2ac..00000000
--- a/tests/lean/External/ExternalFuns.lean
+++ /dev/null
@@ -1,9 +0,0 @@
-import Base
-import External.Types
-import External.Opaque
-
-namespace External
-
-def opaque_defs : OpaqueDefs := sorry
-
-end External
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
index e36987e0..6bfffc33 100644
--- a/tests/lean/External/Funs.lean
+++ b/tests/lean/External/Funs.lean
@@ -2,18 +2,17 @@
 -- [external]: function definitions
 import Base
 import External.Types
-import External.ExternalFuns
+import External.FunsExternal
 open Primitives
-
-namespace External
+namespace external
 
 /- [external::swap] -/
 def swap_fwd
   (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
   do
-    let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st1, _) ← opaque_defs.core_mem_swap_back0 T x y st st0
-    let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
+    let (st0, _) ← core.mem.swap_fwd T x y st
+    let (st1, _) ← core.mem.swap_back0 T x y st st0
+    let (st2, _) ← core.mem.swap_back1 T x y st st1
     Result.ret (st2, ())
 
 /- [external::swap] -/
@@ -22,18 +21,17 @@ def swap_back
   Result (State × (T × T))
   :=
   do
-    let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st2, x0) ← opaque_defs.core_mem_swap_back0 T x y st st1
-    let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
+    let (st1, _) ← core.mem.swap_fwd T x y st
+    let (st2, x0) ← core.mem.swap_back0 T x y st st1
+    let (_, y0) ← core.mem.swap_back1 T x y st st2
     Result.ret (st0, (x0, y0))
 
 /- [external::test_new_non_zero_u32] -/
 def test_new_non_zero_u32_fwd
   (x : U32) (st : State) : Result (State × core_num_nonzero_non_zero_u32_t) :=
   do
-    let (st0, opt) ← opaque_defs.core_num_nonzero_non_zero_u32_new_fwd x st
-    opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t
-      opt st0
+    let (st0, opt) ← core.num.nonzero.NonZeroU32.new_fwd x st
+    core.option.Option.unwrap_fwd core_num_nonzero_non_zero_u32_t opt st0
 
 /- [external::test_vec] -/
 def test_vec_fwd : Result Unit :=
@@ -49,9 +47,9 @@ def test_vec_fwd : Result Unit :=
 def custom_swap_fwd
   (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
   do
-    let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st1, x0) ← opaque_defs.core_mem_swap_back0 T x y st st0
-    let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
+    let (st0, _) ← core.mem.swap_fwd T x y st
+    let (st1, x0) ← core.mem.swap_back0 T x y st st0
+    let (st2, _) ← core.mem.swap_back1 T x y st st1
     Result.ret (st2, x0)
 
 /- [external::custom_swap] -/
@@ -60,9 +58,9 @@ def custom_swap_back
   Result (State × (T × T))
   :=
   do
-    let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st2, _) ← opaque_defs.core_mem_swap_back0 T x y st st1
-    let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
+    let (st1, _) ← core.mem.swap_fwd T x y st
+    let (st2, _) ← core.mem.swap_back0 T x y st st1
+    let (_, y0) ← core.mem.swap_back1 T x y st st2
     Result.ret (st0, (ret0, y0))
 
 /- [external::test_custom_swap] -/
@@ -88,4 +86,4 @@ def test_swap_non_zero_fwd (x : U32) (st : State) : Result (State × U32) :=
     then Result.fail Error.panic
     else Result.ret (st1, x0)
 
-end External
+end external
diff --git a/tests/lean/External/FunsExternal.lean b/tests/lean/External/FunsExternal.lean
new file mode 100644
index 00000000..5326dd77
--- /dev/null
+++ b/tests/lean/External/FunsExternal.lean
@@ -0,0 +1,33 @@
+-- [external]: templates for the external functions.
+import Base
+import External.Types
+open Primitives
+open external
+
+-- TODO: fill those bodies
+
+/- [core::mem::swap] -/
+def core.mem.swap_fwd
+  (T : Type) : T → T → State → Result (State × Unit) :=
+  fun _x _y s => .ret (s, ())
+
+/- [core::mem::swap] -/
+def core.mem.swap_back0
+  (T : Type) : T → T → State → State → Result (State × T) :=
+  fun _x y _s0 s1 => .ret (s1, y)
+
+/- [core::mem::swap] -/
+def core.mem.swap_back1
+  (T : Type) : T → T → State → State → Result (State × T) :=
+  fun x _y _s0 s1 => .ret (s1, x)
+
+/- [core::num::nonzero::NonZeroU32::{14}::new] -/
+def core.num.nonzero.NonZeroU32.new_fwd
+  :
+  U32 → State → Result (State × (Option core_num_nonzero_non_zero_u32_t)) :=
+  fun _ _ => .fail .panic
+
+/- [core::option::Option::{0}::unwrap] -/
+def core.option.Option.unwrap_fwd
+  (T : Type) : Option T → State → Result (State × T) :=
+  fun _ _ => .fail .panic
diff --git a/tests/lean/External/FunsExternal_Template.lean b/tests/lean/External/FunsExternal_Template.lean
new file mode 100644
index 00000000..d6c0eb1d
--- /dev/null
+++ b/tests/lean/External/FunsExternal_Template.lean
@@ -0,0 +1,29 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import External.Types
+open Primitives
+open external
+
+/- [core::mem::swap] -/
+axiom core.mem.swap_fwd
+  (T : Type) : T → T → State → Result (State × Unit)
+
+/- [core::mem::swap] -/
+axiom core.mem.swap_back0
+  (T : Type) : T → T → State → State → Result (State × T)
+
+/- [core::mem::swap] -/
+axiom core.mem.swap_back1
+  (T : Type) : T → T → State → State → Result (State × T)
+
+/- [core::num::nonzero::NonZeroU32::{14}::new] -/
+axiom core.num.nonzero.NonZeroU32.new_fwd
+  :
+  U32 → State → Result (State × (Option core_num_nonzero_non_zero_u32_t))
+
+/- [core::option::Option::{0}::unwrap] -/
+axiom core.option.Option.unwrap_fwd
+  (T : Type) : Option T → State → Result (State × T)
+
diff --git a/tests/lean/External/Opaque.lean b/tests/lean/External/Opaque.lean
index 1c0db095..d0297523 100644
--- a/tests/lean/External/Opaque.lean
+++ b/tests/lean/External/Opaque.lean
@@ -4,29 +4,29 @@ import Base
 import External.Types
 open Primitives
 
-namespace External
+namespace external
 
 structure OpaqueDefs where
   
   /- [core::mem::swap] -/
-  core_mem_swap_fwd (T : Type) : T → T → State → Result (State × Unit)
+  core.mem.swap_fwd (T : Type) : T → T → State → Result (State × Unit)
   
   /- [core::mem::swap] -/
-  core_mem_swap_back0
+  core.mem.swap_back0
     (T : Type) : T → T → State → State → Result (State × T)
   
   /- [core::mem::swap] -/
-  core_mem_swap_back1
+  core.mem.swap_back1
     (T : Type) : T → T → State → State → Result (State × T)
   
   /- [core::num::nonzero::NonZeroU32::{14}::new] -/
-  core_num_nonzero_non_zero_u32_new_fwd
+  core.num.nonzero.NonZeroU32.new_fwd
     :
     U32 → State → Result (State × (Option
       core_num_nonzero_non_zero_u32_t))
   
   /- [core::option::Option::{0}::unwrap] -/
-  core_option_option_unwrap_fwd
+  core.option.Option.unwrap_fwd
     (T : Type) : Option T → State → Result (State × T)
   
-end External
+end external
diff --git a/tests/lean/External/Types.lean b/tests/lean/External/Types.lean
index fda0670e..316f6474 100644
--- a/tests/lean/External/Types.lean
+++ b/tests/lean/External/Types.lean
@@ -2,8 +2,7 @@
 -- [external]: type definitions
 import Base
 open Primitives
-
-namespace External
+namespace external
 
 /- [core::num::nonzero::NonZeroU32] -/
 axiom core_num_nonzero_non_zero_u32_t : Type
@@ -11,4 +10,4 @@ axiom core_num_nonzero_non_zero_u32_t : Type
 /- The state type used in the state-error monad -/
 axiom State : Type
 
-end External
+end external
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
index b4254726..8f54eca8 100644
--- a/tests/lean/Hashmap/Funs.lean
+++ b/tests/lean/Hashmap/Funs.lean
@@ -3,38 +3,37 @@
 import Base
 import Hashmap.Types
 open Primitives
-
-namespace Hashmap
+namespace hashmap
 
 /- [hashmap::hash_key] -/
 def hash_key_fwd (k : Usize) : Result Usize :=
   Result.ret k
 
 /- [hashmap::HashMap::{0}::allocate_slots] -/
-divergent def hash_map_allocate_slots_loop_fwd
+divergent def HashMap.allocate_slots_loop_fwd
   (T : Type) (slots : Vec (list_t T)) (n : Usize) : Result (Vec (list_t T)) :=
   if n > (Usize.ofInt 0 (by intlit))
   then
     do
       let slots0 ← vec_push_back (list_t T) slots list_t.Nil
       let n0 ← n - (Usize.ofInt 1 (by intlit))
-      hash_map_allocate_slots_loop_fwd T slots0 n0
+      HashMap.allocate_slots_loop_fwd T slots0 n0
   else Result.ret slots
 
 /- [hashmap::HashMap::{0}::allocate_slots] -/
-def hash_map_allocate_slots_fwd
+def HashMap.allocate_slots_fwd
   (T : Type) (slots : Vec (list_t T)) (n : Usize) : Result (Vec (list_t T)) :=
-  hash_map_allocate_slots_loop_fwd T slots n
+  HashMap.allocate_slots_loop_fwd T slots n
 
 /- [hashmap::HashMap::{0}::new_with_capacity] -/
-def hash_map_new_with_capacity_fwd
+def HashMap.new_with_capacity_fwd
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
   (max_load_divisor : Usize) :
   Result (hash_map_t T)
   :=
   do
     let v := vec_new (list_t T)
-    let slots ← hash_map_allocate_slots_fwd T v capacity
+    let slots ← HashMap.allocate_slots_fwd T v capacity
     let i ← capacity * max_load_dividend
     let i0 ← i / max_load_divisor
     Result.ret
@@ -46,12 +45,12 @@ def hash_map_new_with_capacity_fwd
       }
 
 /- [hashmap::HashMap::{0}::new] -/
-def hash_map_new_fwd (T : Type) : Result (hash_map_t T) :=
-  hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
+def HashMap.new_fwd (T : Type) : Result (hash_map_t T) :=
+  HashMap.new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
     (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
 
 /- [hashmap::HashMap::{0}::clear] -/
-divergent def hash_map_clear_loop_fwd_back
+divergent def HashMap.clear_loop_fwd_back
   (T : Type) (slots : Vec (list_t T)) (i : Usize) : Result (Vec (list_t T)) :=
   let i0 := vec_len (list_t T) slots
   if i < i0
@@ -59,15 +58,15 @@ divergent def hash_map_clear_loop_fwd_back
     do
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let slots0 ← vec_index_mut_back (list_t T) slots i list_t.Nil
-      hash_map_clear_loop_fwd_back T slots0 i1
+      HashMap.clear_loop_fwd_back T slots0 i1
   else Result.ret slots
 
 /- [hashmap::HashMap::{0}::clear] -/
-def hash_map_clear_fwd_back
+def HashMap.clear_fwd_back
   (T : Type) (self : hash_map_t T) : Result (hash_map_t T) :=
   do
     let v ←
-      hash_map_clear_loop_fwd_back T self.hash_map_slots
+      HashMap.clear_loop_fwd_back T self.hash_map_slots
         (Usize.ofInt 0 (by intlit))
     Result.ret
       {
@@ -78,26 +77,26 @@ def hash_map_clear_fwd_back
       }
 
 /- [hashmap::HashMap::{0}::len] -/
-def hash_map_len_fwd (T : Type) (self : hash_map_t T) : Result Usize :=
+def HashMap.len_fwd (T : Type) (self : hash_map_t T) : Result Usize :=
   Result.ret self.hash_map_num_entries
 
 /- [hashmap::HashMap::{0}::insert_in_list] -/
-divergent def hash_map_insert_in_list_loop_fwd
+divergent def HashMap.insert_in_list_loop_fwd
   (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result Bool :=
   match ls with
   | list_t.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret false
-    else hash_map_insert_in_list_loop_fwd T key value tl
+    else HashMap.insert_in_list_loop_fwd T key value tl
   | list_t.Nil => Result.ret true
 
 /- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_fwd
+def HashMap.insert_in_list_fwd
   (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result Bool :=
-  hash_map_insert_in_list_loop_fwd T key value ls
+  HashMap.insert_in_list_loop_fwd T key value ls
 
 /- [hashmap::HashMap::{0}::insert_in_list] -/
-divergent def hash_map_insert_in_list_loop_back
+divergent def HashMap.insert_in_list_loop_back
   (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result (list_t T) :=
   match ls with
   | list_t.Cons ckey cvalue tl =>
@@ -105,18 +104,18 @@ divergent def hash_map_insert_in_list_loop_back
     then Result.ret (list_t.Cons ckey value tl)
     else
       do
-        let tl0 ← hash_map_insert_in_list_loop_back T key value tl
+        let tl0 ← HashMap.insert_in_list_loop_back T key value tl
         Result.ret (list_t.Cons ckey cvalue tl0)
   | list_t.Nil => let l := list_t.Nil
                   Result.ret (list_t.Cons key value l)
 
 /- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_back
+def HashMap.insert_in_list_back
   (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result (list_t T) :=
-  hash_map_insert_in_list_loop_back T key value ls
+  HashMap.insert_in_list_loop_back T key value ls
 
 /- [hashmap::HashMap::{0}::insert_no_resize] -/
-def hash_map_insert_no_resize_fwd_back
+def HashMap.insert_no_resize_fwd_back
   (T : Type) (self : hash_map_t T) (key : Usize) (value : T) :
   Result (hash_map_t T)
   :=
@@ -125,18 +124,18 @@ def hash_map_insert_no_resize_fwd_back
     let i := vec_len (list_t T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let inserted ← hash_map_insert_in_list_fwd T key value l
+    let inserted ← HashMap.insert_in_list_fwd T key value l
     if inserted
     then
       do
         let i0 ← self.hash_map_num_entries + (Usize.ofInt 1 (by intlit))
-        let l0 ← hash_map_insert_in_list_back T key value l
+        let l0 ← HashMap.insert_in_list_back T key value l
         let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
         Result.ret
           { self with hash_map_num_entries := i0, hash_map_slots := v }
     else
       do
-        let l0 ← hash_map_insert_in_list_back T key value l
+        let l0 ← HashMap.insert_in_list_back T key value l
         let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
         Result.ret { self with hash_map_slots := v }
 
@@ -146,22 +145,22 @@ def core_num_u32_max_body : Result U32 :=
 def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
 
 /- [hashmap::HashMap::{0}::move_elements_from_list] -/
-divergent def hash_map_move_elements_from_list_loop_fwd_back
+divergent def HashMap.move_elements_from_list_loop_fwd_back
   (T : Type) (ntable : hash_map_t T) (ls : list_t T) : Result (hash_map_t T) :=
   match ls with
   | list_t.Cons k v tl =>
     do
-      let ntable0 ← hash_map_insert_no_resize_fwd_back T ntable k v
-      hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
+      let ntable0 ← HashMap.insert_no_resize_fwd_back T ntable k v
+      HashMap.move_elements_from_list_loop_fwd_back T ntable0 tl
   | list_t.Nil => Result.ret ntable
 
 /- [hashmap::HashMap::{0}::move_elements_from_list] -/
-def hash_map_move_elements_from_list_fwd_back
+def HashMap.move_elements_from_list_fwd_back
   (T : Type) (ntable : hash_map_t T) (ls : list_t T) : Result (hash_map_t T) :=
-  hash_map_move_elements_from_list_loop_fwd_back T ntable ls
+  HashMap.move_elements_from_list_loop_fwd_back T ntable ls
 
 /- [hashmap::HashMap::{0}::move_elements] -/
-divergent def hash_map_move_elements_loop_fwd_back
+divergent def HashMap.move_elements_loop_fwd_back
   (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) :
   Result ((hash_map_t T) × (Vec (list_t T)))
   :=
@@ -171,22 +170,22 @@ divergent def hash_map_move_elements_loop_fwd_back
     do
       let l ← vec_index_mut_fwd (list_t T) slots i
       let ls := mem_replace_fwd (list_t T) l list_t.Nil
-      let ntable0 ← hash_map_move_elements_from_list_fwd_back T ntable ls
+      let ntable0 ← HashMap.move_elements_from_list_fwd_back T ntable ls
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let l0 := mem_replace_back (list_t T) l list_t.Nil
       let slots0 ← vec_index_mut_back (list_t T) slots i l0
-      hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
+      HashMap.move_elements_loop_fwd_back T ntable0 slots0 i1
   else Result.ret (ntable, slots)
 
 /- [hashmap::HashMap::{0}::move_elements] -/
-def hash_map_move_elements_fwd_back
+def HashMap.move_elements_fwd_back
   (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) :
   Result ((hash_map_t T) × (Vec (list_t T)))
   :=
-  hash_map_move_elements_loop_fwd_back T ntable slots i
+  HashMap.move_elements_loop_fwd_back T ntable slots i
 
 /- [hashmap::HashMap::{0}::try_resize] -/
-def hash_map_try_resize_fwd_back
+def HashMap.try_resize_fwd_back
   (T : Type) (self : hash_map_t T) : Result (hash_map_t T) :=
   do
     let max_usize ← Scalar.cast .Usize core_num_u32_max_c
@@ -198,9 +197,9 @@ def hash_map_try_resize_fwd_back
     then
       do
         let i2 ← capacity * (Usize.ofInt 2 (by intlit))
-        let ntable ← hash_map_new_with_capacity_fwd T i2 i i0
+        let ntable ← HashMap.new_with_capacity_fwd T i2 i i0
         let (ntable0, _) ←
-          hash_map_move_elements_fwd_back T ntable self.hash_map_slots
+          HashMap.move_elements_fwd_back T ntable self.hash_map_slots
             (Usize.ofInt 0 (by intlit))
         Result.ret
           {
@@ -212,84 +211,84 @@ def hash_map_try_resize_fwd_back
     else Result.ret { self with hash_map_max_load_factor := (i, i0) }
 
 /- [hashmap::HashMap::{0}::insert] -/
-def hash_map_insert_fwd_back
+def HashMap.insert_fwd_back
   (T : Type) (self : hash_map_t T) (key : Usize) (value : T) :
   Result (hash_map_t T)
   :=
   do
-    let self0 ← hash_map_insert_no_resize_fwd_back T self key value
-    let i ← hash_map_len_fwd T self0
+    let self0 ← HashMap.insert_no_resize_fwd_back T self key value
+    let i ← HashMap.len_fwd T self0
     if i > self0.hash_map_max_load
-    then hash_map_try_resize_fwd_back T self0
+    then HashMap.try_resize_fwd_back T self0
     else Result.ret self0
 
 /- [hashmap::HashMap::{0}::contains_key_in_list] -/
-divergent def hash_map_contains_key_in_list_loop_fwd
+divergent def HashMap.contains_key_in_list_loop_fwd
   (T : Type) (key : Usize) (ls : list_t T) : Result Bool :=
   match ls with
   | list_t.Cons ckey t tl =>
     if ckey = key
     then Result.ret true
-    else hash_map_contains_key_in_list_loop_fwd T key tl
+    else HashMap.contains_key_in_list_loop_fwd T key tl
   | list_t.Nil => Result.ret false
 
 /- [hashmap::HashMap::{0}::contains_key_in_list] -/
-def hash_map_contains_key_in_list_fwd
+def HashMap.contains_key_in_list_fwd
   (T : Type) (key : Usize) (ls : list_t T) : Result Bool :=
-  hash_map_contains_key_in_list_loop_fwd T key ls
+  HashMap.contains_key_in_list_loop_fwd T key ls
 
 /- [hashmap::HashMap::{0}::contains_key] -/
-def hash_map_contains_key_fwd
+def HashMap.contains_key_fwd
   (T : Type) (self : hash_map_t T) (key : Usize) : Result Bool :=
   do
     let hash ← hash_key_fwd key
     let i := vec_len (list_t T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod
-    hash_map_contains_key_in_list_fwd T key l
+    HashMap.contains_key_in_list_fwd T key l
 
 /- [hashmap::HashMap::{0}::get_in_list] -/
-divergent def hash_map_get_in_list_loop_fwd
+divergent def HashMap.get_in_list_loop_fwd
   (T : Type) (key : Usize) (ls : list_t T) : Result T :=
   match ls with
   | list_t.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else hash_map_get_in_list_loop_fwd T key tl
+    else HashMap.get_in_list_loop_fwd T key tl
   | list_t.Nil => Result.fail Error.panic
 
 /- [hashmap::HashMap::{0}::get_in_list] -/
-def hash_map_get_in_list_fwd
+def HashMap.get_in_list_fwd
   (T : Type) (key : Usize) (ls : list_t T) : Result T :=
-  hash_map_get_in_list_loop_fwd T key ls
+  HashMap.get_in_list_loop_fwd T key ls
 
 /- [hashmap::HashMap::{0}::get] -/
-def hash_map_get_fwd
+def HashMap.get_fwd
   (T : Type) (self : hash_map_t T) (key : Usize) : Result T :=
   do
     let hash ← hash_key_fwd key
     let i := vec_len (list_t T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod
-    hash_map_get_in_list_fwd T key l
+    HashMap.get_in_list_fwd T key l
 
 /- [hashmap::HashMap::{0}::get_mut_in_list] -/
-divergent def hash_map_get_mut_in_list_loop_fwd
+divergent def HashMap.get_mut_in_list_loop_fwd
   (T : Type) (ls : list_t T) (key : Usize) : Result T :=
   match ls with
   | list_t.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else hash_map_get_mut_in_list_loop_fwd T tl key
+    else HashMap.get_mut_in_list_loop_fwd T tl key
   | list_t.Nil => Result.fail Error.panic
 
 /- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_fwd
+def HashMap.get_mut_in_list_fwd
   (T : Type) (ls : list_t T) (key : Usize) : Result T :=
-  hash_map_get_mut_in_list_loop_fwd T ls key
+  HashMap.get_mut_in_list_loop_fwd T ls key
 
 /- [hashmap::HashMap::{0}::get_mut_in_list] -/
-divergent def hash_map_get_mut_in_list_loop_back
+divergent def HashMap.get_mut_in_list_loop_back
   (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : Result (list_t T) :=
   match ls with
   | list_t.Cons ckey cvalue tl =>
@@ -297,27 +296,27 @@ divergent def hash_map_get_mut_in_list_loop_back
     then Result.ret (list_t.Cons ckey ret0 tl)
     else
       do
-        let tl0 ← hash_map_get_mut_in_list_loop_back T tl key ret0
+        let tl0 ← HashMap.get_mut_in_list_loop_back T tl key ret0
         Result.ret (list_t.Cons ckey cvalue tl0)
   | list_t.Nil => Result.fail Error.panic
 
 /- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_back
+def HashMap.get_mut_in_list_back
   (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : Result (list_t T) :=
-  hash_map_get_mut_in_list_loop_back T ls key ret0
+  HashMap.get_mut_in_list_loop_back T ls key ret0
 
 /- [hashmap::HashMap::{0}::get_mut] -/
-def hash_map_get_mut_fwd
+def HashMap.get_mut_fwd
   (T : Type) (self : hash_map_t T) (key : Usize) : Result T :=
   do
     let hash ← hash_key_fwd key
     let i := vec_len (list_t T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    hash_map_get_mut_in_list_fwd T l key
+    HashMap.get_mut_in_list_fwd T l key
 
 /- [hashmap::HashMap::{0}::get_mut] -/
-def hash_map_get_mut_back
+def HashMap.get_mut_back
   (T : Type) (self : hash_map_t T) (key : Usize) (ret0 : T) :
   Result (hash_map_t T)
   :=
@@ -326,12 +325,12 @@ def hash_map_get_mut_back
     let i := vec_len (list_t T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let l0 ← hash_map_get_mut_in_list_back T l key ret0
+    let l0 ← HashMap.get_mut_in_list_back T l key ret0
     let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
     Result.ret { self with hash_map_slots := v }
 
 /- [hashmap::HashMap::{0}::remove_from_list] -/
-divergent def hash_map_remove_from_list_loop_fwd
+divergent def HashMap.remove_from_list_loop_fwd
   (T : Type) (key : Usize) (ls : list_t T) : Result (Option T) :=
   match ls with
   | list_t.Cons ckey t tl =>
@@ -342,16 +341,16 @@ divergent def hash_map_remove_from_list_loop_fwd
       match mv_ls with
       | list_t.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
       | list_t.Nil => Result.fail Error.panic
-    else hash_map_remove_from_list_loop_fwd T key tl
+    else HashMap.remove_from_list_loop_fwd T key tl
   | list_t.Nil => Result.ret Option.none
 
 /- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_fwd
+def HashMap.remove_from_list_fwd
   (T : Type) (key : Usize) (ls : list_t T) : Result (Option T) :=
-  hash_map_remove_from_list_loop_fwd T key ls
+  HashMap.remove_from_list_loop_fwd T key ls
 
 /- [hashmap::HashMap::{0}::remove_from_list] -/
-divergent def hash_map_remove_from_list_loop_back
+divergent def HashMap.remove_from_list_loop_back
   (T : Type) (key : Usize) (ls : list_t T) : Result (list_t T) :=
   match ls with
   | list_t.Cons ckey t tl =>
@@ -364,24 +363,24 @@ divergent def hash_map_remove_from_list_loop_back
       | list_t.Nil => Result.fail Error.panic
     else
       do
-        let tl0 ← hash_map_remove_from_list_loop_back T key tl
+        let tl0 ← HashMap.remove_from_list_loop_back T key tl
         Result.ret (list_t.Cons ckey t tl0)
   | list_t.Nil => Result.ret list_t.Nil
 
 /- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_back
+def HashMap.remove_from_list_back
   (T : Type) (key : Usize) (ls : list_t T) : Result (list_t T) :=
-  hash_map_remove_from_list_loop_back T key ls
+  HashMap.remove_from_list_loop_back T key ls
 
 /- [hashmap::HashMap::{0}::remove] -/
-def hash_map_remove_fwd
+def HashMap.remove_fwd
   (T : Type) (self : hash_map_t T) (key : Usize) : Result (Option T) :=
   do
     let hash ← hash_key_fwd key
     let i := vec_len (list_t T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let x ← hash_map_remove_from_list_fwd T key l
+    let x ← HashMap.remove_from_list_fwd T key l
     match x with
     | Option.none => Result.ret Option.none
     | Option.some x0 =>
@@ -390,24 +389,24 @@ def hash_map_remove_fwd
         Result.ret (Option.some x0)
 
 /- [hashmap::HashMap::{0}::remove] -/
-def hash_map_remove_back
+def HashMap.remove_back
   (T : Type) (self : hash_map_t T) (key : Usize) : Result (hash_map_t T) :=
   do
     let hash ← hash_key_fwd key
     let i := vec_len (list_t T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let x ← hash_map_remove_from_list_fwd T key l
+    let x ← HashMap.remove_from_list_fwd T key l
     match x with
     | Option.none =>
       do
-        let l0 ← hash_map_remove_from_list_back T key l
+        let l0 ← HashMap.remove_from_list_back T key l
         let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
         Result.ret { self with hash_map_slots := v }
     | Option.some x0 =>
       do
         let i0 ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit))
-        let l0 ← hash_map_remove_from_list_back T key l
+        let l0 ← HashMap.remove_from_list_back T key l
         let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
         Result.ret
           { self with hash_map_num_entries := i0, hash_map_slots := v }
@@ -415,34 +414,33 @@ def hash_map_remove_back
 /- [hashmap::test1] -/
 def test1_fwd : Result Unit :=
   do
-    let hm ← hash_map_new_fwd U64
+    let hm ← HashMap.new_fwd U64
     let hm0 ←
-      hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
+      HashMap.insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
         (U64.ofInt 42 (by intlit))
     let hm1 ←
-      hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
+      HashMap.insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
         (U64.ofInt 18 (by intlit))
     let hm2 ←
-      hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
+      HashMap.insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
         (U64.ofInt 138 (by intlit))
     let hm3 ←
-      hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
+      HashMap.insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
         (U64.ofInt 256 (by intlit))
-    let i ← hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
+    let i ← HashMap.get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
     if not (i = (U64.ofInt 18 (by intlit)))
     then Result.fail Error.panic
     else
       do
         let hm4 ←
-          hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
+          HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
             (U64.ofInt 56 (by intlit))
-        let i0 ← hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
+        let i0 ← HashMap.get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
         if not (i0 = (U64.ofInt 56 (by intlit)))
         then Result.fail Error.panic
         else
           do
-            let x ←
-              hash_map_remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
+            let x ← HashMap.remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
             match x with
             | Option.none => Result.fail Error.panic
             | Option.some x0 =>
@@ -451,21 +449,21 @@ def test1_fwd : Result Unit :=
               else
                 do
                   let hm5 ←
-                    hash_map_remove_back U64 hm4 (Usize.ofInt 1024 (by intlit))
+                    HashMap.remove_back U64 hm4 (Usize.ofInt 1024 (by intlit))
                   let i1 ←
-                    hash_map_get_fwd U64 hm5 (Usize.ofInt 0 (by intlit))
+                    HashMap.get_fwd U64 hm5 (Usize.ofInt 0 (by intlit))
                   if not (i1 = (U64.ofInt 42 (by intlit)))
                   then Result.fail Error.panic
                   else
                     do
                       let i2 ←
-                        hash_map_get_fwd U64 hm5 (Usize.ofInt 128 (by intlit))
+                        HashMap.get_fwd U64 hm5 (Usize.ofInt 128 (by intlit))
                       if not (i2 = (U64.ofInt 18 (by intlit)))
                       then Result.fail Error.panic
                       else
                         do
                           let i3 ←
-                            hash_map_get_fwd U64 hm5
+                            HashMap.get_fwd U64 hm5
                               (Usize.ofInt 1056 (by intlit))
                           if not (i3 = (U64.ofInt 256 (by intlit)))
                           then Result.fail Error.panic
@@ -474,4 +472,4 @@ def test1_fwd : Result Unit :=
 /- Unit test for [hashmap::test1] -/
 #assert (test1_fwd == .ret ())
 
-end Hashmap
+end hashmap
diff --git a/tests/lean/Hashmap/Types.lean b/tests/lean/Hashmap/Types.lean
index 0aec6acf..75a6500f 100644
--- a/tests/lean/Hashmap/Types.lean
+++ b/tests/lean/Hashmap/Types.lean
@@ -2,8 +2,7 @@
 -- [hashmap]: type definitions
 import Base
 open Primitives
-
-namespace Hashmap
+namespace hashmap
 
 /- [hashmap::List] -/
 inductive list_t (T : Type) :=
@@ -17,4 +16,4 @@ structure hash_map_t (T : Type) where
   hash_map_max_load : Usize
   hash_map_slots : Vec (list_t T)
 
-end Hashmap
+end hashmap
diff --git a/tests/lean/HashmapMain/ExternalFuns.lean b/tests/lean/HashmapMain/ExternalFuns.lean
deleted file mode 100644
index bc831158..00000000
--- a/tests/lean/HashmapMain/ExternalFuns.lean
+++ /dev/null
@@ -1,9 +0,0 @@
-import Base
-import HashmapMain.Types
-import HashmapMain.Opaque
-
-namespace HashmapMain
-
-def opaque_defs : OpaqueDefs := by sorry
-
-end HashmapMain
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
index 34a0eca1..06929431 100644
--- a/tests/lean/HashmapMain/Funs.lean
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -2,17 +2,16 @@
 -- [hashmap_main]: function definitions
 import Base
 import HashmapMain.Types
-import HashmapMain.ExternalFuns
+import HashmapMain.FunsExternal
 open Primitives
-
-namespace HashmapMain
+namespace hashmap_main
 
 /- [hashmap_main::hashmap::hash_key] -/
-def hashmap_hash_key_fwd (k : Usize) : Result Usize :=
+def hashmap.hash_key_fwd (k : Usize) : Result Usize :=
   Result.ret k
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-divergent def hashmap_hash_map_allocate_slots_loop_fwd
+divergent def hashmap.HashMap.allocate_slots_loop_fwd
   (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) :
   Result (Vec (hashmap_list_t T))
   :=
@@ -21,25 +20,25 @@ divergent def hashmap_hash_map_allocate_slots_loop_fwd
     do
       let slots0 ← vec_push_back (hashmap_list_t T) slots hashmap_list_t.Nil
       let n0 ← n - (Usize.ofInt 1 (by intlit))
-      hashmap_hash_map_allocate_slots_loop_fwd T slots0 n0
+      hashmap.HashMap.allocate_slots_loop_fwd T slots0 n0
   else Result.ret slots
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-def hashmap_hash_map_allocate_slots_fwd
+def hashmap.HashMap.allocate_slots_fwd
   (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) :
   Result (Vec (hashmap_list_t T))
   :=
-  hashmap_hash_map_allocate_slots_loop_fwd T slots n
+  hashmap.HashMap.allocate_slots_loop_fwd T slots n
 
 /- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] -/
-def hashmap_hash_map_new_with_capacity_fwd
+def hashmap.HashMap.new_with_capacity_fwd
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
   (max_load_divisor : Usize) :
   Result (hashmap_hash_map_t T)
   :=
   do
     let v := vec_new (hashmap_list_t T)
-    let slots ← hashmap_hash_map_allocate_slots_fwd T v capacity
+    let slots ← hashmap.HashMap.allocate_slots_fwd T v capacity
     let i ← capacity * max_load_dividend
     let i0 ← i / max_load_divisor
     Result.ret
@@ -52,12 +51,12 @@ def hashmap_hash_map_new_with_capacity_fwd
       }
 
 /- [hashmap_main::hashmap::HashMap::{0}::new] -/
-def hashmap_hash_map_new_fwd (T : Type) : Result (hashmap_hash_map_t T) :=
-  hashmap_hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
+def hashmap.HashMap.new_fwd (T : Type) : Result (hashmap_hash_map_t T) :=
+  hashmap.HashMap.new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
     (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
 
 /- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-divergent def hashmap_hash_map_clear_loop_fwd_back
+divergent def hashmap.HashMap.clear_loop_fwd_back
   (T : Type) (slots : Vec (hashmap_list_t T)) (i : Usize) :
   Result (Vec (hashmap_list_t T))
   :=
@@ -68,15 +67,15 @@ divergent def hashmap_hash_map_clear_loop_fwd_back
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let slots0 ←
         vec_index_mut_back (hashmap_list_t T) slots i hashmap_list_t.Nil
-      hashmap_hash_map_clear_loop_fwd_back T slots0 i1
+      hashmap.HashMap.clear_loop_fwd_back T slots0 i1
   else Result.ret slots
 
 /- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-def hashmap_hash_map_clear_fwd_back
+def hashmap.HashMap.clear_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
   do
     let v ←
-      hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots
+      hashmap.HashMap.clear_loop_fwd_back T self.hashmap_hash_map_slots
         (Usize.ofInt 0 (by intlit))
     Result.ret
       {
@@ -87,27 +86,27 @@ def hashmap_hash_map_clear_fwd_back
       }
 
 /- [hashmap_main::hashmap::HashMap::{0}::len] -/
-def hashmap_hash_map_len_fwd
+def hashmap.HashMap.len_fwd
   (T : Type) (self : hashmap_hash_map_t T) : Result Usize :=
   Result.ret self.hashmap_hash_map_num_entries
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-divergent def hashmap_hash_map_insert_in_list_loop_fwd
+divergent def hashmap.HashMap.insert_in_list_loop_fwd
   (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : Result Bool :=
   match ls with
   | hashmap_list_t.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret false
-    else hashmap_hash_map_insert_in_list_loop_fwd T key value tl
+    else hashmap.HashMap.insert_in_list_loop_fwd T key value tl
   | hashmap_list_t.Nil => Result.ret true
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_fwd
+def hashmap.HashMap.insert_in_list_fwd
   (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : Result Bool :=
-  hashmap_hash_map_insert_in_list_loop_fwd T key value ls
+  hashmap.HashMap.insert_in_list_loop_fwd T key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-divergent def hashmap_hash_map_insert_in_list_loop_back
+divergent def hashmap.HashMap.insert_in_list_loop_back
   (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
   Result (hashmap_list_t T)
   :=
@@ -117,37 +116,37 @@ divergent def hashmap_hash_map_insert_in_list_loop_back
     then Result.ret (hashmap_list_t.Cons ckey value tl)
     else
       do
-        let tl0 ← hashmap_hash_map_insert_in_list_loop_back T key value tl
+        let tl0 ← hashmap.HashMap.insert_in_list_loop_back T key value tl
         Result.ret (hashmap_list_t.Cons ckey cvalue tl0)
   | hashmap_list_t.Nil =>
     let l := hashmap_list_t.Nil
     Result.ret (hashmap_list_t.Cons key value l)
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_back
+def hashmap.HashMap.insert_in_list_back
   (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
   Result (hashmap_list_t T)
   :=
-  hashmap_hash_map_insert_in_list_loop_back T key value ls
+  hashmap.HashMap.insert_in_list_loop_back T key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] -/
-def hashmap_hash_map_insert_no_resize_fwd_back
+def hashmap.HashMap.insert_no_resize_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) :
   Result (hashmap_hash_map_t T)
   :=
   do
-    let hash ← hashmap_hash_key_fwd key
+    let hash ← hashmap.hash_key_fwd key
     let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let inserted ← hashmap_hash_map_insert_in_list_fwd T key value l
+    let inserted ← hashmap.HashMap.insert_in_list_fwd T key value l
     if inserted
     then
       do
         let i0 ← self.hashmap_hash_map_num_entries +
           (Usize.ofInt 1 (by intlit))
-        let l0 ← hashmap_hash_map_insert_in_list_back T key value l
+        let l0 ← hashmap.HashMap.insert_in_list_back T key value l
         let v ←
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
             hash_mod l0
@@ -159,7 +158,7 @@ def hashmap_hash_map_insert_no_resize_fwd_back
           }
     else
       do
-        let l0 ← hashmap_hash_map_insert_in_list_back T key value l
+        let l0 ← hashmap.HashMap.insert_in_list_back T key value l
         let v ←
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
             hash_mod l0
@@ -171,26 +170,26 @@ def core_num_u32_max_body : Result U32 :=
 def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-divergent def hashmap_hash_map_move_elements_from_list_loop_fwd_back
+divergent def hashmap.HashMap.move_elements_from_list_loop_fwd_back
   (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
   Result (hashmap_hash_map_t T)
   :=
   match ls with
   | hashmap_list_t.Cons k v tl =>
     do
-      let ntable0 ← hashmap_hash_map_insert_no_resize_fwd_back T ntable k v
-      hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
+      let ntable0 ← hashmap.HashMap.insert_no_resize_fwd_back T ntable k v
+      hashmap.HashMap.move_elements_from_list_loop_fwd_back T ntable0 tl
   | hashmap_list_t.Nil => Result.ret ntable
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-def hashmap_hash_map_move_elements_from_list_fwd_back
+def hashmap.HashMap.move_elements_from_list_fwd_back
   (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
   Result (hashmap_hash_map_t T)
   :=
-  hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable ls
+  hashmap.HashMap.move_elements_from_list_loop_fwd_back T ntable ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-divergent def hashmap_hash_map_move_elements_loop_fwd_back
+divergent def hashmap.HashMap.move_elements_loop_fwd_back
   (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
   (i : Usize) :
   Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T)))
@@ -202,23 +201,23 @@ divergent def hashmap_hash_map_move_elements_loop_fwd_back
       let l ← vec_index_mut_fwd (hashmap_list_t T) slots i
       let ls := mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.Nil
       let ntable0 ←
-        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls
+        hashmap.HashMap.move_elements_from_list_fwd_back T ntable ls
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let l0 := mem_replace_back (hashmap_list_t T) l hashmap_list_t.Nil
       let slots0 ← vec_index_mut_back (hashmap_list_t T) slots i l0
-      hashmap_hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
+      hashmap.HashMap.move_elements_loop_fwd_back T ntable0 slots0 i1
   else Result.ret (ntable, slots)
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-def hashmap_hash_map_move_elements_fwd_back
+def hashmap.HashMap.move_elements_fwd_back
   (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
   (i : Usize) :
   Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T)))
   :=
-  hashmap_hash_map_move_elements_loop_fwd_back T ntable slots i
+  hashmap.HashMap.move_elements_loop_fwd_back T ntable slots i
 
 /- [hashmap_main::hashmap::HashMap::{0}::try_resize] -/
-def hashmap_hash_map_try_resize_fwd_back
+def hashmap.HashMap.try_resize_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
   do
     let max_usize ← Scalar.cast .Usize core_num_u32_max_c
@@ -230,9 +229,9 @@ def hashmap_hash_map_try_resize_fwd_back
     then
       do
         let i2 ← capacity * (Usize.ofInt 2 (by intlit))
-        let ntable ← hashmap_hash_map_new_with_capacity_fwd T i2 i i0
+        let ntable ← hashmap.HashMap.new_with_capacity_fwd T i2 i i0
         let (ntable0, _) ←
-          hashmap_hash_map_move_elements_fwd_back T ntable
+          hashmap.HashMap.move_elements_fwd_back T ntable
             self.hashmap_hash_map_slots (Usize.ofInt 0 (by intlit))
         Result.ret
           {
@@ -244,86 +243,86 @@ def hashmap_hash_map_try_resize_fwd_back
     else Result.ret { self with hashmap_hash_map_max_load_factor := (i, i0) }
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert] -/
-def hashmap_hash_map_insert_fwd_back
+def hashmap.HashMap.insert_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) :
   Result (hashmap_hash_map_t T)
   :=
   do
-    let self0 ← hashmap_hash_map_insert_no_resize_fwd_back T self key value
-    let i ← hashmap_hash_map_len_fwd T self0
+    let self0 ← hashmap.HashMap.insert_no_resize_fwd_back T self key value
+    let i ← hashmap.HashMap.len_fwd T self0
     if i > self0.hashmap_hash_map_max_load
-    then hashmap_hash_map_try_resize_fwd_back T self0
+    then hashmap.HashMap.try_resize_fwd_back T self0
     else Result.ret self0
 
 /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-divergent def hashmap_hash_map_contains_key_in_list_loop_fwd
+divergent def hashmap.HashMap.contains_key_in_list_loop_fwd
   (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result Bool :=
   match ls with
   | hashmap_list_t.Cons ckey t tl =>
     if ckey = key
     then Result.ret true
-    else hashmap_hash_map_contains_key_in_list_loop_fwd T key tl
+    else hashmap.HashMap.contains_key_in_list_loop_fwd T key tl
   | hashmap_list_t.Nil => Result.ret false
 
 /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-def hashmap_hash_map_contains_key_in_list_fwd
+def hashmap.HashMap.contains_key_in_list_fwd
   (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result Bool :=
-  hashmap_hash_map_contains_key_in_list_loop_fwd T key ls
+  hashmap.HashMap.contains_key_in_list_loop_fwd T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::contains_key] -/
-def hashmap_hash_map_contains_key_fwd
+def hashmap.HashMap.contains_key_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result Bool :=
   do
-    let hash ← hashmap_hash_key_fwd key
+    let hash ← hashmap.hash_key_fwd key
     let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    hashmap_hash_map_contains_key_in_list_fwd T key l
+    hashmap.HashMap.contains_key_in_list_fwd T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-divergent def hashmap_hash_map_get_in_list_loop_fwd
+divergent def hashmap.HashMap.get_in_list_loop_fwd
   (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result T :=
   match ls with
   | hashmap_list_t.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else hashmap_hash_map_get_in_list_loop_fwd T key tl
+    else hashmap.HashMap.get_in_list_loop_fwd T key tl
   | hashmap_list_t.Nil => Result.fail Error.panic
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-def hashmap_hash_map_get_in_list_fwd
+def hashmap.HashMap.get_in_list_fwd
   (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result T :=
-  hashmap_hash_map_get_in_list_loop_fwd T key ls
+  hashmap.HashMap.get_in_list_loop_fwd T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::get] -/
-def hashmap_hash_map_get_fwd
+def hashmap.HashMap.get_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap_hash_key_fwd key
+    let hash ← hashmap.hash_key_fwd key
     let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    hashmap_hash_map_get_in_list_fwd T key l
+    hashmap.HashMap.get_in_list_fwd T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-divergent def hashmap_hash_map_get_mut_in_list_loop_fwd
+divergent def hashmap.HashMap.get_mut_in_list_loop_fwd
   (T : Type) (ls : hashmap_list_t T) (key : Usize) : Result T :=
   match ls with
   | hashmap_list_t.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else hashmap_hash_map_get_mut_in_list_loop_fwd T tl key
+    else hashmap.HashMap.get_mut_in_list_loop_fwd T tl key
   | hashmap_list_t.Nil => Result.fail Error.panic
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_fwd
+def hashmap.HashMap.get_mut_in_list_fwd
   (T : Type) (ls : hashmap_list_t T) (key : Usize) : Result T :=
-  hashmap_hash_map_get_mut_in_list_loop_fwd T ls key
+  hashmap.HashMap.get_mut_in_list_loop_fwd T ls key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-divergent def hashmap_hash_map_get_mut_in_list_loop_back
+divergent def hashmap.HashMap.get_mut_in_list_loop_back
   (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) :
   Result (hashmap_list_t T)
   :=
@@ -333,47 +332,47 @@ divergent def hashmap_hash_map_get_mut_in_list_loop_back
     then Result.ret (hashmap_list_t.Cons ckey ret0 tl)
     else
       do
-        let tl0 ← hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0
+        let tl0 ← hashmap.HashMap.get_mut_in_list_loop_back T tl key ret0
         Result.ret (hashmap_list_t.Cons ckey cvalue tl0)
   | hashmap_list_t.Nil => Result.fail Error.panic
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_back
+def hashmap.HashMap.get_mut_in_list_back
   (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) :
   Result (hashmap_list_t T)
   :=
-  hashmap_hash_map_get_mut_in_list_loop_back T ls key ret0
+  hashmap.HashMap.get_mut_in_list_loop_back T ls key ret0
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
-def hashmap_hash_map_get_mut_fwd
+def hashmap.HashMap.get_mut_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap_hash_key_fwd key
+    let hash ← hashmap.hash_key_fwd key
     let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    hashmap_hash_map_get_mut_in_list_fwd T l key
+    hashmap.HashMap.get_mut_in_list_fwd T l key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
-def hashmap_hash_map_get_mut_back
+def hashmap.HashMap.get_mut_back
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (ret0 : T) :
   Result (hashmap_hash_map_t T)
   :=
   do
-    let hash ← hashmap_hash_key_fwd key
+    let hash ← hashmap.hash_key_fwd key
     let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let l0 ← hashmap_hash_map_get_mut_in_list_back T l key ret0
+    let l0 ← hashmap.HashMap.get_mut_in_list_back T l key ret0
     let v ←
       vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
         hash_mod l0
     Result.ret { self with hashmap_hash_map_slots := v }
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-divergent def hashmap_hash_map_remove_from_list_loop_fwd
+divergent def hashmap.HashMap.remove_from_list_loop_fwd
   (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result (Option T) :=
   match ls with
   | hashmap_list_t.Cons ckey t tl =>
@@ -385,16 +384,16 @@ divergent def hashmap_hash_map_remove_from_list_loop_fwd
       match mv_ls with
       | hashmap_list_t.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
       | hashmap_list_t.Nil => Result.fail Error.panic
-    else hashmap_hash_map_remove_from_list_loop_fwd T key tl
+    else hashmap.HashMap.remove_from_list_loop_fwd T key tl
   | hashmap_list_t.Nil => Result.ret Option.none
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_fwd
+def hashmap.HashMap.remove_from_list_fwd
   (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result (Option T) :=
-  hashmap_hash_map_remove_from_list_loop_fwd T key ls
+  hashmap.HashMap.remove_from_list_loop_fwd T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-divergent def hashmap_hash_map_remove_from_list_loop_back
+divergent def hashmap.HashMap.remove_from_list_loop_back
   (T : Type) (key : Usize) (ls : hashmap_list_t T) :
   Result (hashmap_list_t T)
   :=
@@ -410,27 +409,27 @@ divergent def hashmap_hash_map_remove_from_list_loop_back
       | hashmap_list_t.Nil => Result.fail Error.panic
     else
       do
-        let tl0 ← hashmap_hash_map_remove_from_list_loop_back T key tl
+        let tl0 ← hashmap.HashMap.remove_from_list_loop_back T key tl
         Result.ret (hashmap_list_t.Cons ckey t tl0)
   | hashmap_list_t.Nil => Result.ret hashmap_list_t.Nil
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_back
+def hashmap.HashMap.remove_from_list_back
   (T : Type) (key : Usize) (ls : hashmap_list_t T) :
   Result (hashmap_list_t T)
   :=
-  hashmap_hash_map_remove_from_list_loop_back T key ls
+  hashmap.HashMap.remove_from_list_loop_back T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove] -/
-def hashmap_hash_map_remove_fwd
+def hashmap.HashMap.remove_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result (Option T) :=
   do
-    let hash ← hashmap_hash_key_fwd key
+    let hash ← hashmap.hash_key_fwd key
     let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let x ← hashmap_hash_map_remove_from_list_fwd T key l
+    let x ← hashmap.HashMap.remove_from_list_fwd T key l
     match x with
     | Option.none => Result.ret Option.none
     | Option.some x0 =>
@@ -440,21 +439,21 @@ def hashmap_hash_map_remove_fwd
         Result.ret (Option.some x0)
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove] -/
-def hashmap_hash_map_remove_back
+def hashmap.HashMap.remove_back
   (T : Type) (self : hashmap_hash_map_t T) (key : Usize) :
   Result (hashmap_hash_map_t T)
   :=
   do
-    let hash ← hashmap_hash_key_fwd key
+    let hash ← hashmap.hash_key_fwd key
     let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let x ← hashmap_hash_map_remove_from_list_fwd T key l
+    let x ← hashmap.HashMap.remove_from_list_fwd T key l
     match x with
     | Option.none =>
       do
-        let l0 ← hashmap_hash_map_remove_from_list_back T key l
+        let l0 ← hashmap.HashMap.remove_from_list_back T key l
         let v ←
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
             hash_mod l0
@@ -463,7 +462,7 @@ def hashmap_hash_map_remove_back
       do
         let i0 ← self.hashmap_hash_map_num_entries -
           (Usize.ofInt 1 (by intlit))
-        let l0 ← hashmap_hash_map_remove_from_list_back T key l
+        let l0 ← hashmap.HashMap.remove_from_list_back T key l
         let v ←
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
             hash_mod l0
@@ -475,38 +474,37 @@ def hashmap_hash_map_remove_back
           }
 
 /- [hashmap_main::hashmap::test1] -/
-def hashmap_test1_fwd : Result Unit :=
+def hashmap.test1_fwd : Result Unit :=
   do
-    let hm ← hashmap_hash_map_new_fwd U64
+    let hm ← hashmap.HashMap.new_fwd U64
     let hm0 ←
-      hashmap_hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
+      hashmap.HashMap.insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
         (U64.ofInt 42 (by intlit))
     let hm1 ←
-      hashmap_hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
+      hashmap.HashMap.insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
         (U64.ofInt 18 (by intlit))
     let hm2 ←
-      hashmap_hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
+      hashmap.HashMap.insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
         (U64.ofInt 138 (by intlit))
     let hm3 ←
-      hashmap_hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
+      hashmap.HashMap.insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
         (U64.ofInt 256 (by intlit))
-    let i ← hashmap_hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
+    let i ← hashmap.HashMap.get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
     if not (i = (U64.ofInt 18 (by intlit)))
     then Result.fail Error.panic
     else
       do
         let hm4 ←
-          hashmap_hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
+          hashmap.HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
             (U64.ofInt 56 (by intlit))
         let i0 ←
-          hashmap_hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
+          hashmap.HashMap.get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
         if not (i0 = (U64.ofInt 56 (by intlit)))
         then Result.fail Error.panic
         else
           do
             let x ←
-              hashmap_hash_map_remove_fwd U64 hm4
-                (Usize.ofInt 1024 (by intlit))
+              hashmap.HashMap.remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
             match x with
             | Option.none => Result.fail Error.panic
             | Option.some x0 =>
@@ -515,39 +513,38 @@ def hashmap_test1_fwd : Result Unit :=
               else
                 do
                   let hm5 ←
-                    hashmap_hash_map_remove_back U64 hm4
+                    hashmap.HashMap.remove_back U64 hm4
                       (Usize.ofInt 1024 (by intlit))
                   let i1 ←
-                    hashmap_hash_map_get_fwd U64 hm5
-                      (Usize.ofInt 0 (by intlit))
+                    hashmap.HashMap.get_fwd U64 hm5 (Usize.ofInt 0 (by intlit))
                   if not (i1 = (U64.ofInt 42 (by intlit)))
                   then Result.fail Error.panic
                   else
                     do
                       let i2 ←
-                        hashmap_hash_map_get_fwd U64 hm5
+                        hashmap.HashMap.get_fwd U64 hm5
                           (Usize.ofInt 128 (by intlit))
                       if not (i2 = (U64.ofInt 18 (by intlit)))
                       then Result.fail Error.panic
                       else
                         do
                           let i3 ←
-                            hashmap_hash_map_get_fwd U64 hm5
+                            hashmap.HashMap.get_fwd U64 hm5
                               (Usize.ofInt 1056 (by intlit))
                           if not (i3 = (U64.ofInt 256 (by intlit)))
                           then Result.fail Error.panic
                           else Result.ret ()
 
 /- Unit test for [hashmap_main::hashmap::test1] -/
-#assert (hashmap_test1_fwd == .ret ())
+#assert (hashmap.test1_fwd == .ret ())
 
 /- [hashmap_main::insert_on_disk] -/
 def insert_on_disk_fwd
   (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
   do
-    let (st0, hm) ← opaque_defs.hashmap_utils_deserialize_fwd st
-    let hm0 ← hashmap_hash_map_insert_fwd_back U64 hm key value
-    let (st1, _) ← opaque_defs.hashmap_utils_serialize_fwd hm0 st0
+    let (st0, hm) ← hashmap_utils.deserialize_fwd st
+    let hm0 ← hashmap.HashMap.insert_fwd_back U64 hm key value
+    let (st1, _) ← hashmap_utils.serialize_fwd hm0 st0
     Result.ret (st1, ())
 
 /- [hashmap_main::main] -/
@@ -557,4 +554,4 @@ def main_fwd : Result Unit :=
 /- Unit test for [hashmap_main::main] -/
 #assert (main_fwd == .ret ())
 
-end HashmapMain
+end hashmap_main
diff --git a/tests/lean/HashmapMain/FunsExternal.lean b/tests/lean/HashmapMain/FunsExternal.lean
new file mode 100644
index 00000000..d917b485
--- /dev/null
+++ b/tests/lean/HashmapMain/FunsExternal.lean
@@ -0,0 +1,17 @@
+-- [hashmap_main]: templates for the external functions.
+import Base
+import HashmapMain.Types
+open Primitives
+open hashmap_main
+
+-- TODO: fill those bodies
+
+/- [hashmap_main::hashmap_utils::deserialize] -/
+def hashmap_utils.deserialize_fwd
+  : State → Result (State × (hashmap_hash_map_t U64)) :=
+  fun _ => .fail .panic
+
+/- [hashmap_main::hashmap_utils::serialize] -/
+def hashmap_utils.serialize_fwd
+  : hashmap_hash_map_t U64 → State → Result (State × Unit) :=
+  fun _ _ => .fail .panic
diff --git a/tests/lean/HashmapMain/FunsExternal_Template.lean b/tests/lean/HashmapMain/FunsExternal_Template.lean
new file mode 100644
index 00000000..86286373
--- /dev/null
+++ b/tests/lean/HashmapMain/FunsExternal_Template.lean
@@ -0,0 +1,16 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import HashmapMain.Types
+open Primitives
+open hashmap_main
+
+/- [hashmap_main::hashmap_utils::deserialize] -/
+axiom hashmap_utils.deserialize_fwd
+  : State → Result (State × (hashmap_hash_map_t U64))
+
+/- [hashmap_main::hashmap_utils::serialize] -/
+axiom hashmap_utils.serialize_fwd
+  : hashmap_hash_map_t U64 → State → Result (State × Unit)
+
diff --git a/tests/lean/HashmapMain/Opaque.lean b/tests/lean/HashmapMain/Opaque.lean
index 10e4d8bd..abf04c94 100644
--- a/tests/lean/HashmapMain/Opaque.lean
+++ b/tests/lean/HashmapMain/Opaque.lean
@@ -4,16 +4,16 @@ import Base
 import HashmapMain.Types
 open Primitives
 
-namespace HashmapMain
+namespace hashmap_main
 
 structure OpaqueDefs where
   
   /- [hashmap_main::hashmap_utils::deserialize] -/
-  hashmap_utils_deserialize_fwd
+  hashmap_utils.deserialize_fwd
     : State → Result (State × (hashmap_hash_map_t U64))
   
   /- [hashmap_main::hashmap_utils::serialize] -/
-  hashmap_utils_serialize_fwd
+  hashmap_utils.serialize_fwd
     : hashmap_hash_map_t U64 → State → Result (State × Unit)
   
-end HashmapMain
+end hashmap_main
diff --git a/tests/lean/HashmapMain/Types.lean b/tests/lean/HashmapMain/Types.lean
index b91ff3a7..16641146 100644
--- a/tests/lean/HashmapMain/Types.lean
+++ b/tests/lean/HashmapMain/Types.lean
@@ -2,8 +2,7 @@
 -- [hashmap_main]: type definitions
 import Base
 open Primitives
-
-namespace HashmapMain
+namespace hashmap_main
 
 /- [hashmap_main::hashmap::List] -/
 inductive hashmap_list_t (T : Type) :=
@@ -20,4 +19,4 @@ structure hashmap_hash_map_t (T : Type) where
 /- The state type used in the state-error monad -/
 axiom State : Type
 
-end HashmapMain
+end hashmap_main
diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
index 9e084327..694f5450 100644
--- a/tests/lean/Loops/Funs.lean
+++ b/tests/lean/Loops/Funs.lean
@@ -3,8 +3,7 @@
 import Base
 import Loops.Types
 open Primitives
-
-namespace Loops
+namespace loops
 
 /- [loops::sum] -/
 divergent def sum_loop_fwd (max : U32) (i : U32) (s : U32) : Result U32 :=
@@ -624,4 +623,4 @@ def list_nth_shared_mut_loop_pair_merge_back
   :=
   list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
 
-end Loops
+end loops
diff --git a/tests/lean/Loops/Types.lean b/tests/lean/Loops/Types.lean
index ca0403e9..5b5ed31f 100644
--- a/tests/lean/Loops/Types.lean
+++ b/tests/lean/Loops/Types.lean
@@ -2,12 +2,11 @@
 -- [loops]: type definitions
 import Base
 open Primitives
-
-namespace Loops
+namespace loops
 
 /- [loops::List] -/
 inductive list_t (T : Type) :=
 | Cons : T → list_t T → list_t T
 | Nil : list_t T
 
-end Loops
+end loops
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
index 769bb311..67abc8f6 100644
--- a/tests/lean/NoNestedBorrows.lean
+++ b/tests/lean/NoNestedBorrows.lean
@@ -2,8 +2,7 @@
 -- [no_nested_borrows]
 import Base
 open Primitives
-
-namespace NoNestedBorrows
+namespace no_nested_borrows
 
 /- [no_nested_borrows::Pair] -/
 structure pair_t (T1 T2 : Type) where
@@ -541,4 +540,4 @@ def test_shared_borrow_enum1_fwd (l : list_t U32) : Result U32 :=
 def test_shared_borrow_enum2_fwd : Result U32 :=
   Result.ret (U32.ofInt 0 (by intlit))
 
-end NoNestedBorrows
+end no_nested_borrows
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
index edcb5c1b..c34941ef 100644
--- a/tests/lean/Paper.lean
+++ b/tests/lean/Paper.lean
@@ -2,8 +2,7 @@
 -- [paper]
 import Base
 open Primitives
-
-namespace Paper
+namespace paper
 
 /- [paper::ref_incr] -/
 def ref_incr_fwd_back (x : I32) : Result I32 :=
@@ -125,4 +124,4 @@ def call_choose_fwd (p : (U32 × U32)) : Result U32 :=
     let (px0, _) ← choose_back U32 true px py pz0
     Result.ret px0
 
-end Paper
+end paper
diff --git a/tests/lean/PoloniusList.lean b/tests/lean/PoloniusList.lean
index 0f2a05e3..0ff01b47 100644
--- a/tests/lean/PoloniusList.lean
+++ b/tests/lean/PoloniusList.lean
@@ -2,8 +2,7 @@
 -- [polonius_list]
 import Base
 open Primitives
-
-namespace PoloniusList
+namespace polonius_list
 
 /- [polonius_list::List] -/
 inductive list_t (T : Type) :=
@@ -33,4 +32,4 @@ divergent def get_list_at_x_back
         Result.ret (list_t.Cons hd tl0)
   | list_t.Nil => Result.ret ret0
 
-end PoloniusList
+end polonius_list
diff --git a/tests/lean/Tests.lean b/tests/lean/Tests.lean
deleted file mode 100644
index 9b12270e..00000000
--- a/tests/lean/Tests.lean
+++ /dev/null
@@ -1,9 +0,0 @@
-import BetreeMain
-import Constants
-import External
-import Hashmap
-import HashmapMain
-import Loops
-import NoNestedBorrows
-import Paper
-import PoloniusList
diff --git a/tests/lean/lakefile.lean b/tests/lean/lakefile.lean
index 217e533f..ae63b129 100644
--- a/tests/lean/lakefile.lean
+++ b/tests/lean/lakefile.lean
@@ -8,15 +8,12 @@ require Base from "../../backends/lean"
 
 package «tests» {}
 
-@[default_target]
-lean_lib «Tests» {}
-
-lean_lib betreeMain
-lean_lib constants
-lean_lib external
-lean_lib hashmap
-lean_lib hashmapMain
-lean_lib loops
-lean_lib noNestedBorrows
-lean_lib paper
-lean_lib poloniusList
+@[default_target] lean_lib betreeMain
+@[default_target] lean_lib constants
+@[default_target] lean_lib external
+@[default_target] lean_lib hashmap
+@[default_target] lean_lib hashmapMain
+@[default_target] lean_lib loops
+@[default_target] lean_lib noNestedBorrows
+@[default_target] lean_lib paper
+@[default_target] lean_lib poloniusList