Modify some options and update the Makefile

1 files changed, 784 insertions, 0 deletions

diff --git a/tests/fstar/misc/Loops.fst b/tests/fstar/misc/Loops.fst
new file mode 100644
index 00000000..823acdd4
--- /dev/null
+++ b/tests/fstar/misc/Loops.fst
@@ -0,0 +1,784 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [loops] *)
+module Loops
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [loops::sum]: decreases clause *)
+unfold let sum_loop_decreases (max : u32) (i : u32) (s : u32) : nat = admit ()
+
+(** [loops::sum]: loop 0: forward function *)
+let rec sum_loop
+  (max : u32) (i : u32) (s : u32) :
+  Tot (result u32) (decreases (sum_loop_decreases max i s))
+  =
+  if i < max
+  then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop max i0 s0
+  else u32_mul s 2
+
+(** [loops::sum]: forward function *)
+let sum (max : u32) : result u32 =
+  sum_loop max 0 0
+
+(** [loops::sum_with_mut_borrows]: decreases clause *)
+unfold
+let sum_with_mut_borrows_loop_decreases (max : u32) (mi : u32) (ms : u32) : nat
+  =
+  admit ()
+
+(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
+let rec sum_with_mut_borrows_loop
+  (max : u32) (mi : u32) (ms : u32) :
+  Tot (result u32) (decreases (sum_with_mut_borrows_loop_decreases max mi ms))
+  =
+  if mi < max
+  then
+    let* ms0 = u32_add ms mi in
+    let* mi0 = u32_add mi 1 in
+    sum_with_mut_borrows_loop max mi0 ms0
+  else u32_mul ms 2
+
+(** [loops::sum_with_mut_borrows]: forward function *)
+let sum_with_mut_borrows (max : u32) : result u32 =
+  sum_with_mut_borrows_loop max 0 0
+
+(** [loops::sum_with_shared_borrows]: decreases clause *)
+unfold
+let sum_with_shared_borrows_loop_decreases (max : u32) (i : u32) (s : u32) :
+  nat =
+  admit ()
+
+(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
+let rec sum_with_shared_borrows_loop
+  (max : u32) (i : u32) (s : u32) :
+  Tot (result u32) (decreases (sum_with_shared_borrows_loop_decreases max i s))
+  =
+  if i < max
+  then
+    let* i0 = u32_add i 1 in
+    let* s0 = u32_add s i0 in
+    sum_with_shared_borrows_loop max i0 s0
+  else u32_mul s 2
+
+(** [loops::sum_with_shared_borrows]: forward function *)
+let sum_with_shared_borrows (max : u32) : result u32 =
+  sum_with_shared_borrows_loop max 0 0
+
+(** [loops::clear]: decreases clause *)
+unfold
+let clear_loop_decreases (v : alloc_vec_Vec u32) (i : usize) : nat = admit ()
+
+(** [loops::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+let rec clear_loop
+  (v : alloc_vec_Vec u32) (i : usize) :
+  Tot (result (alloc_vec_Vec u32)) (decreases (clear_loop_decreases v i))
+  =
+  let i0 = alloc_vec_Vec_len u32 v in
+  if i < i0
+  then
+    let* i1 = usize_add i 1 in
+    let* v0 =
+      alloc_vec_Vec_index_mut_back u32 usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst u32) v i 0 in
+    clear_loop v0 i1
+  else Return v
+
+(** [loops::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) =
+  clear_loop v 0
+
+(** [loops::List] *)
+type list_t (t : Type0) =
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
+
+(** [loops::list_mem]: decreases clause *)
+unfold let list_mem_loop_decreases (x : u32) (ls : list_t u32) : nat = admit ()
+
+(** [loops::list_mem]: loop 0: forward function *)
+let rec list_mem_loop
+  (x : u32) (ls : list_t u32) :
+  Tot (result bool) (decreases (list_mem_loop_decreases x ls))
+  =
+  begin match ls with
+  | List_Cons y tl -> if y = x then Return true else list_mem_loop x tl
+  | List_Nil -> Return false
+  end
+
+(** [loops::list_mem]: forward function *)
+let list_mem (x : u32) (ls : list_t u32) : result bool =
+  list_mem_loop x ls
+
+(** [loops::list_nth_mut_loop]: decreases clause *)
+unfold
+let list_nth_mut_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
+  nat =
+  admit ()
+
+(** [loops::list_nth_mut_loop]: loop 0: forward function *)
+let rec list_nth_mut_loop_loop
+  (t : Type0) (ls : list_t t) (i : u32) :
+  Tot (result t) (decreases (list_nth_mut_loop_loop_decreases t ls i))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i0 = u32_sub i 1 in list_nth_mut_loop_loop t tl i0
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop]: forward function *)
+let list_nth_mut_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
+  list_nth_mut_loop_loop t ls i
+
+(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
+let rec list_nth_mut_loop_loop_back
+  (t : Type0) (ls : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return (List_Cons ret tl)
+    else
+      let* i0 = u32_sub i 1 in
+      let* tl0 = list_nth_mut_loop_loop_back t tl i0 ret in
+      Return (List_Cons x tl0)
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop]: backward function 0 *)
+let list_nth_mut_loop_back
+  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
+  list_nth_mut_loop_loop_back t ls i ret
+
+(** [loops::list_nth_shared_loop]: decreases clause *)
+unfold
+let list_nth_shared_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
+  nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop]: loop 0: forward function *)
+let rec list_nth_shared_loop_loop
+  (t : Type0) (ls : list_t t) (i : u32) :
+  Tot (result t) (decreases (list_nth_shared_loop_loop_decreases t ls i))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop t tl i0
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop]: forward function *)
+let list_nth_shared_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
+  list_nth_shared_loop_loop t ls i
+
+(** [loops::get_elem_mut]: decreases clause *)
+unfold
+let get_elem_mut_loop_decreases (x : usize) (ls : list_t usize) : nat =
+  admit ()
+
+(** [loops::get_elem_mut]: loop 0: forward function *)
+let rec get_elem_mut_loop
+  (x : usize) (ls : list_t usize) :
+  Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls))
+  =
+  begin match ls with
+  | List_Cons y tl -> if y = x then Return y else get_elem_mut_loop x tl
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::get_elem_mut]: forward function *)
+let get_elem_mut
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
+  let* l =
+    alloc_vec_Vec_index_mut (list_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
+      slots 0 in
+  get_elem_mut_loop x l
+
+(** [loops::get_elem_mut]: loop 0: backward function 0 *)
+let rec get_elem_mut_loop_back
+  (x : usize) (ls : list_t usize) (ret : usize) :
+  Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
+  =
+  begin match ls with
+  | List_Cons y tl ->
+    if y = x
+    then Return (List_Cons ret tl)
+    else let* tl0 = get_elem_mut_loop_back x tl ret in Return (List_Cons y tl0)
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::get_elem_mut]: backward function 0 *)
+let get_elem_mut_back
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) (ret : usize) :
+  result (alloc_vec_Vec (list_t usize))
+  =
+  let* l =
+    alloc_vec_Vec_index_mut (list_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
+      slots 0 in
+  let* l0 = get_elem_mut_loop_back x l ret in
+  alloc_vec_Vec_index_mut_back (list_t usize) usize
+    (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) slots
+    0 l0
+
+(** [loops::get_elem_shared]: decreases clause *)
+unfold
+let get_elem_shared_loop_decreases (x : usize) (ls : list_t usize) : nat =
+  admit ()
+
+(** [loops::get_elem_shared]: loop 0: forward function *)
+let rec get_elem_shared_loop
+  (x : usize) (ls : list_t usize) :
+  Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls))
+  =
+  begin match ls with
+  | List_Cons y tl -> if y = x then Return y else get_elem_shared_loop x tl
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::get_elem_shared]: forward function *)
+let get_elem_shared
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
+  let* l =
+    alloc_vec_Vec_index (list_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
+      slots 0 in
+  get_elem_shared_loop x l
+
+(** [loops::id_mut]: forward function *)
+let id_mut (t : Type0) (ls : list_t t) : result (list_t t) =
+  Return ls
+
+(** [loops::id_mut]: backward function 0 *)
+let id_mut_back
+  (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
+  Return ret
+
+(** [loops::id_shared]: forward function *)
+let id_shared (t : Type0) (ls : list_t t) : result (list_t t) =
+  Return ls
+
+(** [loops::list_nth_mut_loop_with_id]: decreases clause *)
+unfold
+let list_nth_mut_loop_with_id_loop_decreases (t : Type0) (i : u32)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
+let rec list_nth_mut_loop_with_id_loop
+  (t : Type0) (i : u32) (ls : list_t t) :
+  Tot (result t) (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i0 = u32_sub i 1 in list_nth_mut_loop_with_id_loop t i0 tl
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_with_id]: forward function *)
+let list_nth_mut_loop_with_id
+  (t : Type0) (ls : list_t t) (i : u32) : result t =
+  let* ls0 = id_mut t ls in list_nth_mut_loop_with_id_loop t i ls0
+
+(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
+let rec list_nth_mut_loop_with_id_loop_back
+  (t : Type0) (i : u32) (ls : list_t t) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return (List_Cons ret tl)
+    else
+      let* i0 = u32_sub i 1 in
+      let* tl0 = list_nth_mut_loop_with_id_loop_back t i0 tl ret in
+      Return (List_Cons x tl0)
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
+let list_nth_mut_loop_with_id_back
+  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
+  let* ls0 = id_mut t ls in
+  let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in
+  id_mut_back t ls l
+
+(** [loops::list_nth_shared_loop_with_id]: decreases clause *)
+unfold
+let list_nth_shared_loop_with_id_loop_decreases (t : Type0) (i : u32)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
+let rec list_nth_shared_loop_with_id_loop
+  (t : Type0) (i : u32) (ls : list_t t) :
+  Tot (result t)
+  (decreases (list_nth_shared_loop_with_id_loop_decreases t i ls))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i0 = u32_sub i 1 in list_nth_shared_loop_with_id_loop t i0 tl
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop_with_id]: forward function *)
+let list_nth_shared_loop_with_id
+  (t : Type0) (ls : list_t t) (i : u32) : result t =
+  let* ls0 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls0
+
+(** [loops::list_nth_mut_loop_pair]: decreases clause *)
+unfold
+let list_nth_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
+let rec list_nth_mut_loop_pair_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair]: forward function *)
+let list_nth_mut_loop_pair
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_mut_loop_pair_loop t ls0 ls1 i
+
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
+let rec list_nth_mut_loop_pair_loop_back'a
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl0)
+      else
+        let* i0 = u32_sub i 1 in
+        let* tl00 = list_nth_mut_loop_pair_loop_back'a t tl0 tl1 i0 ret in
+        Return (List_Cons x0 tl00)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
+let list_nth_mut_loop_pair_back'a
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret
+
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
+let rec list_nth_mut_loop_pair_loop_back'b
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl1)
+      else
+        let* i0 = u32_sub i 1 in
+        let* tl10 = list_nth_mut_loop_pair_loop_back'b t tl0 tl1 i0 ret in
+        Return (List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
+let list_nth_mut_loop_pair_back'b
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
+
+(** [loops::list_nth_shared_loop_pair]: decreases clause *)
+unfold
+let list_nth_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
+let rec list_nth_shared_loop_pair_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_shared_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else let* i0 = u32_sub i 1 in list_nth_shared_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop_pair]: forward function *)
+let list_nth_shared_loop_pair
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_shared_loop_pair_loop t ls0 ls1 i
+
+(** [loops::list_nth_mut_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_mut_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
+let rec list_nth_mut_loop_pair_merge_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
+let list_nth_mut_loop_pair_merge
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_mut_loop_pair_merge_loop t ls0 ls1 i
+
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
+let rec list_nth_mut_loop_pair_merge_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
+  Tot (result ((list_t t) & (list_t t)))
+  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then let (x, x2) = ret in Return (List_Cons x tl0, List_Cons x2 tl1)
+      else
+        let* i0 = u32_sub i 1 in
+        let* (tl00, tl10) =
+          list_nth_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
+        Return (List_Cons x0 tl00, List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
+let list_nth_mut_loop_pair_merge_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
+  result ((list_t t) & (list_t t))
+  =
+  list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
+
+(** [loops::list_nth_shared_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_shared_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
+let rec list_nth_shared_loop_pair_merge_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i0 = u32_sub i 1 in
+        list_nth_shared_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
+let list_nth_shared_loop_pair_merge
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_shared_loop_pair_merge_loop t ls0 ls1 i
+
+(** [loops::list_nth_mut_shared_loop_pair]: decreases clause *)
+unfold
+let list_nth_mut_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
+let rec list_nth_mut_shared_loop_pair_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i0 = u32_sub i 1 in
+        list_nth_mut_shared_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
+let list_nth_mut_shared_loop_pair
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_mut_shared_loop_pair_loop t ls0 ls1 i
+
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
+let rec list_nth_mut_shared_loop_pair_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl0)
+      else
+        let* i0 = u32_sub i 1 in
+        let* tl00 = list_nth_mut_shared_loop_pair_loop_back t tl0 tl1 i0 ret in
+        Return (List_Cons x0 tl00)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
+let list_nth_mut_shared_loop_pair_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_mut_shared_loop_pair_merge_loop_decreases (t : Type0)
+  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
+let rec list_nth_mut_shared_loop_pair_merge_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i0 = u32_sub i 1 in
+        list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
+let list_nth_mut_shared_loop_pair_merge
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_mut_shared_loop_pair_merge_loop t ls0 ls1 i
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
+let rec list_nth_mut_shared_loop_pair_merge_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl0)
+      else
+        let* i0 = u32_sub i 1 in
+        let* tl00 =
+          list_nth_mut_shared_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
+        Return (List_Cons x0 tl00)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
+let list_nth_mut_shared_loop_pair_merge_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret
+
+(** [loops::list_nth_shared_mut_loop_pair]: decreases clause *)
+unfold
+let list_nth_shared_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
+let rec list_nth_shared_mut_loop_pair_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i0 = u32_sub i 1 in
+        list_nth_shared_mut_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
+let list_nth_shared_mut_loop_pair
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_shared_mut_loop_pair_loop t ls0 ls1 i
+
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
+let rec list_nth_shared_mut_loop_pair_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl1)
+      else
+        let* i0 = u32_sub i 1 in
+        let* tl10 = list_nth_shared_mut_loop_pair_loop_back t tl0 tl1 i0 ret in
+        Return (List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
+let list_nth_shared_mut_loop_pair_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_shared_mut_loop_pair_merge_loop_decreases (t : Type0)
+  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
+let rec list_nth_shared_mut_loop_pair_merge_loop
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  Tot (result (t & t))
+  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i0 = u32_sub i 1 in
+        list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
+let list_nth_shared_mut_loop_pair_merge
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
+  list_nth_shared_mut_loop_pair_merge_loop t ls0 ls1 i
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
+let rec list_nth_shared_mut_loop_pair_merge_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl1)
+      else
+        let* i0 = u32_sub i 1 in
+        let* tl10 =
+          list_nth_shared_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
+        Return (List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
+let list_nth_shared_mut_loop_pair_merge_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_shared_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
+