diff --git a/lib/arith.sail b/lib/arith.sail
index 202d2ec5a..974b2c8c3 100644
--- a/lib/arith.sail
+++ b/lib/arith.sail
@@ -51,16 +51,16 @@ $include <flow.sail>
 
 // ***** Addition *****
 
-val add_atom = pure {ocaml: "add_int", interpreter: "add_int", lem: "integerAdd", coq: "Z.add", _: "add_int"} : forall 'n 'm.
+val add_atom = pure {ocaml: "add_int", interpreter: "add_int", lem: "integerAdd", coq: "Z.add", lean: "HAdd.hAdd", _: "add_int"} : forall 'n 'm.
   (int('n), int('m)) -> int('n + 'm)
 
-val add_int = pure {ocaml: "add_int", interpreter: "add_int", lem: "integerAdd", coq: "Z.add",lean: "Int.add",  _: "add_int"} : (int, int) -> int
+val add_int = pure {ocaml: "add_int", interpreter: "add_int", lem: "integerAdd", coq: "Z.add", lean: "Int.add",  _: "add_int"} : (int, int) -> int
 
 overload operator + = {add_atom, add_int}
 
 // ***** Subtraction *****
 
-val sub_atom = pure {ocaml: "sub_int", interpreter: "sub_int", lem: "integerMinus", coq: "Z.sub", _: "sub_int"} : forall 'n 'm.
+val sub_atom = pure {ocaml: "sub_int", interpreter: "sub_int", lem: "integerMinus", coq: "Z.sub", lean: "HSub.hSub", _: "sub_int"} : forall 'n 'm.
   (int('n), int('m)) -> int('n - 'm)
 
 val sub_int = pure {ocaml: "sub_int", interpreter: "sub_int", lem: "integerMinus", coq: "Z.sub", lean: "Int.sub", _: "sub_int"} : (int, int) -> int
@@ -71,6 +71,7 @@ val sub_nat = pure {
   ocaml: "(fun (x,y) -> let n = sub_int (x,y) in if Big_int.less_equal n Big_int.zero then Big_int.zero else n)",
   lem: "integerMinus",
   coq: "Z.sub",
+  lean: "HSub.hSub",
   _: "sub_nat"
 } : (nat, nat) -> nat
 
diff --git a/lib/vector.sail b/lib/vector.sail
index 59c29d43d..87b911b46 100644
--- a/lib/vector.sail
+++ b/lib/vector.sail
@@ -299,6 +299,7 @@ val subrange_bits = pure {
   interpreter: "subrange",
   lem: "subrange_vec_dec",
   coq: "subrange_vec_dec",
+  lean: "Sail.BitVec.extractLsb",
   _: "vector_subrange"
 } : forall ('n : Int) ('m : Int) ('o : Int), 0 <= 'o <= 'm < 'n.
   (bits('n), int('m), int('o)) -> bits('m - 'o + 1)
@@ -321,6 +322,7 @@ val update_subrange_bits = pure {
   interpreter: "update_subrange",
   lem: "update_subrange_vec_dec",
   coq: "update_subrange_vec_dec",
+  lean: "Sail.BitVec.updateSubrange",
   _: "vector_update_subrange"
 } : forall 'n 'm 'o, 0 <= 'o <= 'm < 'n. (bits('n), int('m), int('o), bits('m - ('o - 1))) -> bits('n)
 $else
diff --git a/src/sail_lean_backend/Sail/Sail.lean b/src/sail_lean_backend/Sail/Sail.lean
index 8cf943fdb..dc3dc9f92 100644
--- a/src/sail_lean_backend/Sail/Sail.lean
+++ b/src/sail_lean_backend/Sail/Sail.lean
@@ -19,5 +19,26 @@ def truncate {w : Nat} (x : BitVec w) (w' : Nat) : BitVec w' :=
 def truncateLsb {w : Nat} (x : BitVec w) (w' : Nat) : BitVec w' :=
   x.extractLsb' (w - w') w'
 
+def extractLsb {w : Nat} (x : BitVec w) (hi lo : Nat) : BitVec (hi - lo + 1) :=
+  x.extractLsb hi lo
+
+def updateSubrange' {w : Nat} (x : BitVec w) (start len : Nat) (y : BitVec len) : BitVec w :=
+  let mask := ~~~(((BitVec.allOnes len).zeroExtend w) <<< start)
+  let y' := mask ||| ((y.zeroExtend w) <<< start)
+  x &&& y'
+
+def updateSubrange {w : Nat} (x : BitVec w) (hi lo : Nat) (y : BitVec (hi - lo + 1)) : BitVec w :=
+  updateSubrange' x lo _ y
+
 end BitVec
 end Sail
+
+structure RegisterRef (regstate regval a : Type) where
+  name : String
+  read_from : regstate -> a
+  write_to : a -> regstate -> regstate
+  of_regval : regval -> Option a
+  regval_of : a -> regval
+
+def undefined_bitvector (w : Nat) : BitVec w :=
+  0
diff --git a/src/sail_lean_backend/pretty_print_lean.ml b/src/sail_lean_backend/pretty_print_lean.ml
index 868714246..624ba7fab 100644
--- a/src/sail_lean_backend/pretty_print_lean.ml
+++ b/src/sail_lean_backend/pretty_print_lean.ml
@@ -137,12 +137,21 @@ let rec doc_typ ctxt (Typ_aux (t, _) as typ) =
       parens (string "BitVec " ^^ doc_nexp ctxt m)
   | Typ_app (Id_aux (Id "atom", _), [A_aux (A_nexp (Nexp_aux (Nexp_var ki, _)), _)]) ->
       string "Int" (* TODO This probably has to be generalized *)
+  | Typ_app (Id_aux (Id "register", _), t_app) ->
+      string "RegisterRef Unit Unit "
+      (* TODO: Replace units with real types. *) ^^ separate_map comma (doc_typ_app ctxt) t_app
   | Typ_app (Id_aux (Id "implicit", _), [A_aux (A_nexp (Nexp_aux (Nexp_var ki, _)), _)]) ->
       underscore (* TODO check if the type of implicit arguments can really be always inferred *)
   | Typ_tuple ts -> parens (separate_map (space ^^ string "×" ^^ space) (doc_typ ctxt) ts)
   | Typ_id (Id_aux (Id id, _)) -> string id
   | _ -> failwith ("Type " ^ string_of_typ_con typ ^ " " ^ string_of_typ typ ^ " not translatable yet.")
 
+and doc_typ_app ctxt (A_aux (t, _) as typ) =
+  match t with
+  | A_typ t' -> doc_typ ctxt t'
+  | A_bool nc -> failwith ("Constraint " ^ string_of_n_constraint nc ^ "not translatable yet.")
+  | A_nexp m -> doc_nexp ctxt m
+
 let rec captured_typ_var ((i, Typ_aux (t, _)) as typ) =
   match t with
   | Typ_app (Id_aux (Id "atom", _), [A_aux (A_nexp (Nexp_aux (Nexp_var ki, _)), _)])
@@ -274,8 +283,17 @@ let rec doc_exp ctxt (E_aux (e, (l, annot)) as full_exp) =
         | _ -> failwith "Let pattern not translatable yet."
       in
       nest 2 (flow (break 1) [string "let"; string id; coloneq; doc_exp ctxt lexp]) ^^ hardline ^^ doc_exp ctxt e
+  | E_struct fexps ->
+      let args = List.map (doc_fexp ctxt) fexps in
+      braces (space ^^ nest 2 (separate hardline args) ^^ space)
+  | E_field (exp, id) -> doc_exp ctxt exp ^^ dot ^^ doc_id_ctor id
+  | E_struct_update (exp, fexps) ->
+      let args = List.map (doc_fexp ctxt) fexps in
+      braces (space ^^ doc_exp ctxt exp ^^ string " with " ^^ separate (comma ^^ space) args ^^ space)
   | _ -> failwith ("Expression " ^ string_of_exp_con full_exp ^ " " ^ string_of_exp full_exp ^ " not translatable yet.")
 
+and doc_fexp ctxt (FE_aux (FE_fexp (field, exp), _)) = doc_id_ctor field ^^ string " := " ^^ doc_exp ctxt exp
+
 let doc_binder ctxt i t =
   let paranthesizer =
     match t with
diff --git a/test/lean/bitfield.expected.lean b/test/lean/bitfield.expected.lean
new file mode 100644
index 000000000..b100161a8
--- /dev/null
+++ b/test/lean/bitfield.expected.lean
@@ -0,0 +1,69 @@
+import Out.Sail.Sail
+
+open Sail
+
+def cr_type := (BitVec 8)
+
+def undefined_cr_type (lit : Unit) : SailM (BitVec 8) :=
+  return ((undefined_bitvector 8) : (BitVec 8))
+
+def Mk_cr_type (v : (BitVec 8)) : (BitVec 8) :=
+  v
+
+def _get_cr_type_bits (v : (BitVec 8)) : (BitVec 8) :=
+  (Sail.BitVec.extractLsb v (HSub.hSub 8 1) 0)
+
+def _update_cr_type_bits (v : (BitVec 8)) (x : (BitVec 8)) : (BitVec 8) :=
+  (Sail.BitVec.updateSubrange v (HSub.hSub 8 1) 0 x)
+
+def _set_cr_type_bits (r_ref : RegisterRef Unit Unit (BitVec 8)) (v : (BitVec 8)) : SailM Unit :=
+  return sorry
+
+def _get_cr_type_CR0 (v : (BitVec 8)) : (BitVec 4) :=
+  (Sail.BitVec.extractLsb v 7 4)
+
+def _update_cr_type_CR0 (v : (BitVec 8)) (x : (BitVec 4)) : (BitVec 8) :=
+  (Sail.BitVec.updateSubrange v 7 4 x)
+
+def _set_cr_type_CR0 (r_ref : RegisterRef Unit Unit (BitVec 8)) (v : (BitVec 4)) : SailM Unit :=
+  return sorry
+
+def _get_cr_type_CR1 (v : (BitVec 8)) : (BitVec 2) :=
+  (Sail.BitVec.extractLsb v 3 2)
+
+def _update_cr_type_CR1 (v : (BitVec 8)) (x : (BitVec 2)) : (BitVec 8) :=
+  (Sail.BitVec.updateSubrange v 3 2 x)
+
+def _set_cr_type_CR1 (r_ref : RegisterRef Unit Unit (BitVec 8)) (v : (BitVec 2)) : SailM Unit :=
+  return sorry
+
+def _get_cr_type_CR3 (v : (BitVec 8)) : (BitVec 2) :=
+  (Sail.BitVec.extractLsb v 1 0)
+
+def _update_cr_type_CR3 (v : (BitVec 8)) (x : (BitVec 2)) : (BitVec 8) :=
+  (Sail.BitVec.updateSubrange v 1 0 x)
+
+def _set_cr_type_CR3 (r_ref : RegisterRef Unit Unit (BitVec 8)) (v : (BitVec 2)) : SailM Unit :=
+  return sorry
+
+def _get_cr_type_GT (v : (BitVec 8)) : (BitVec 1) :=
+  (Sail.BitVec.extractLsb v 6 6)
+
+def _update_cr_type_GT (v : (BitVec 8)) (x : (BitVec 1)) : (BitVec 8) :=
+  (Sail.BitVec.updateSubrange v 6 6 x)
+
+def _set_cr_type_GT (r_ref : RegisterRef Unit Unit (BitVec 8)) (v : (BitVec 1)) : SailM Unit :=
+  return sorry
+
+def _get_cr_type_LT (v : (BitVec 8)) : (BitVec 1) :=
+  (Sail.BitVec.extractLsb v 7 7)
+
+def _update_cr_type_LT (v : (BitVec 8)) (x : (BitVec 1)) : (BitVec 8) :=
+  (Sail.BitVec.updateSubrange v 7 7 x)
+
+def _set_cr_type_LT (r_ref : RegisterRef Unit Unit (BitVec 8)) (v : (BitVec 1)) : SailM Unit :=
+  return sorry
+
+def initialize_registers : Unit :=
+  ()
+
diff --git a/test/lean/bitfield.sail b/test/lean/bitfield.sail
new file mode 100644
index 000000000..2969f5927
--- /dev/null
+++ b/test/lean/bitfield.sail
@@ -0,0 +1,11 @@
+default Order dec
+
+$include <prelude.sail>
+
+bitfield cr_type : bits(8) = {
+  CR0 : 7 .. 4,
+  LT  : 7,
+  GT  : 6,
+  CR1 : 3 .. 2,
+  CR3 : 1 .. 0
+}
diff --git a/test/lean/struct.expected.lean b/test/lean/struct.expected.lean
index e3ba05431..60424c7cc 100644
--- a/test/lean/struct.expected.lean
+++ b/test/lean/struct.expected.lean
@@ -4,11 +4,26 @@ open Sail
 
 structure My_struct where
   field1 : Int
-  field2 : Int
+  field2 : (BitVec 1)
 
 def undefined_My_struct (lit : Unit) : SailM My_struct :=
   return sorry
 
+def struct_field2 (s : My_struct) : (BitVec 1) :=
+  s.field2
+
+def struct_update_field2 (s : My_struct) (b : (BitVec 1)) : My_struct :=
+  { s with field2 := b }
+
+/-- Type quantifiers: i : Int -/
+def struct_update_both_fields (s : My_struct) (i : Int) (b : (BitVec 1)) : My_struct :=
+  { s with field1 := i, field2 := b }
+
+/-- Type quantifiers: i : Int -/
+def mk_struct (i : Int) (b : (BitVec 1)) : My_struct :=
+  { field1 := i
+    field2 := b }
+
 def initialize_registers : Unit :=
   ()
 
diff --git a/test/lean/struct.lean.expected b/test/lean/struct.lean.expected
deleted file mode 100644
index eb29e9f6c..000000000
--- a/test/lean/struct.lean.expected
+++ /dev/null
@@ -1,3 +0,0 @@
-structure My_struct where
-  field1 : Int
-  field2 : Int
diff --git a/test/lean/struct.sail b/test/lean/struct.sail
index a4470e820..9853b7d11 100644
--- a/test/lean/struct.sail
+++ b/test/lean/struct.sail
@@ -4,6 +4,28 @@ $include <prelude.sail>
 
 struct My_struct = {
   field1 : int,
-  field2 : int,
+  field2 : bit,
 }
 
+val struct_field2 : My_struct -> bit
+function struct_field2(s) = {
+  s.field2
+}
+
+val struct_update_field2 : (My_struct, bit) -> My_struct
+function struct_update_field2(s, b) = {
+  { s with field2 = b }
+}
+
+val struct_update_both_fields : (My_struct, int, bit) -> My_struct
+function struct_update_both_fields(s, i, b) = {
+  { s with field1 = i, field2 = b }
+}
+
+val mk_struct : (int, bit) -> My_struct
+function mk_struct(i, b) = {
+  struct { 
+    field1 = i,
+    field2 = b
+  }
+}
\ No newline at end of file