Reorganize the Lean tests

1 files changed, 624 insertions, 0 deletions

diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
new file mode 100644
index 00000000..7d5f7595
--- /dev/null
+++ b/tests/lean/Loops/Funs.lean
@@ -0,0 +1,624 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: function definitions
+import Base
+import Loops.Types
+open Primitives
+
+/- [loops::sum] -/
+divergent def sum_loop_fwd (max : U32) (i : U32) (s : U32) : Result U32 :=
+  if i < max
+  then
+    do
+      let s0 ← s + i
+      let i0 ← i + (U32.ofInt 1 (by intlit))
+      sum_loop_fwd max i0 s0
+  else s * (U32.ofInt 2 (by intlit))
+
+/- [loops::sum] -/
+def sum_fwd (max : U32) : Result U32 :=
+  sum_loop_fwd max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit))
+
+/- [loops::sum_with_mut_borrows] -/
+divergent def sum_with_mut_borrows_loop_fwd
+  (max : U32) (mi : U32) (ms : U32) : Result U32 :=
+  if mi < max
+  then
+    do
+      let ms0 ← ms + mi
+      let mi0 ← mi + (U32.ofInt 1 (by intlit))
+      sum_with_mut_borrows_loop_fwd max mi0 ms0
+  else ms * (U32.ofInt 2 (by intlit))
+
+/- [loops::sum_with_mut_borrows] -/
+def sum_with_mut_borrows_fwd (max : U32) : Result U32 :=
+  sum_with_mut_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
+    (U32.ofInt 0 (by intlit))
+
+/- [loops::sum_with_shared_borrows] -/
+divergent def sum_with_shared_borrows_loop_fwd
+  (max : U32) (i : U32) (s : U32) : Result U32 :=
+  if i < max
+  then
+    do
+      let i0 ← i + (U32.ofInt 1 (by intlit))
+      let s0 ← s + i0
+      sum_with_shared_borrows_loop_fwd max i0 s0
+  else s * (U32.ofInt 2 (by intlit))
+
+/- [loops::sum_with_shared_borrows] -/
+def sum_with_shared_borrows_fwd (max : U32) : Result U32 :=
+  sum_with_shared_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
+    (U32.ofInt 0 (by intlit))
+
+/- [loops::clear] -/
+divergent def clear_loop_fwd_back
+  (v : Vec U32) (i : Usize) : Result (Vec U32) :=
+  let i0 := vec_len U32 v
+  if i < i0
+  then
+    do
+      let i1 ← i + (Usize.ofInt 1 (by intlit))
+      let v0 ← vec_index_mut_back U32 v i (U32.ofInt 0 (by intlit))
+      clear_loop_fwd_back v0 i1
+  else Result.ret v
+
+/- [loops::clear] -/
+def clear_fwd_back (v : Vec U32) : Result (Vec U32) :=
+  clear_loop_fwd_back v (Usize.ofInt 0 (by intlit))
+
+/- [loops::list_mem] -/
+divergent def list_mem_loop_fwd (x : U32) (ls : list_t U32) : Result Bool :=
+  match h: ls with
+  | list_t.Cons y tl =>
+    if y = x
+    then Result.ret true
+    else list_mem_loop_fwd x tl
+  | list_t.Nil => Result.ret false
+
+/- [loops::list_mem] -/
+def list_mem_fwd (x : U32) (ls : list_t U32) : Result Bool :=
+  list_mem_loop_fwd x ls
+
+/- [loops::list_nth_mut_loop] -/
+divergent def list_nth_mut_loop_loop_fwd
+  (T : Type) (ls : list_t T) (i : U32) : Result T :=
+  match h: ls with
+  | list_t.Cons x tl =>
+    if i = (U32.ofInt 0 (by intlit))
+    then Result.ret x
+    else
+      do
+        let i0 ← i - (U32.ofInt 1 (by intlit))
+        list_nth_mut_loop_loop_fwd T tl i0
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
+  list_nth_mut_loop_loop_fwd T ls i
+
+/- [loops::list_nth_mut_loop] -/
+divergent def list_nth_mut_loop_loop_back
+  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
+  match h: ls with
+  | list_t.Cons x tl =>
+    if i = (U32.ofInt 0 (by intlit))
+    then Result.ret (list_t.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1 (by intlit))
+        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
+        Result.ret (list_t.Cons x tl0)
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_back
+  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
+  list_nth_mut_loop_loop_back T ls i ret0
+
+/- [loops::list_nth_shared_loop] -/
+divergent def list_nth_shared_loop_loop_fwd
+  (T : Type) (ls : list_t T) (i : U32) : Result T :=
+  match h: ls with
+  | list_t.Cons x tl =>
+    if i = (U32.ofInt 0 (by intlit))
+    then Result.ret x
+    else
+      do
+        let i0 ← i - (U32.ofInt 1 (by intlit))
+        list_nth_shared_loop_loop_fwd T tl i0
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop] -/
+def list_nth_shared_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
+  list_nth_shared_loop_loop_fwd T ls i
+
+/- [loops::get_elem_mut] -/
+divergent def get_elem_mut_loop_fwd
+  (x : Usize) (ls : list_t Usize) : Result Usize :=
+  match h: ls with
+  | list_t.Cons y tl =>
+    if y = x
+    then Result.ret y
+    else get_elem_mut_loop_fwd x tl
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_fwd (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
+  do
+    let l ←
+      vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
+    get_elem_mut_loop_fwd x l
+
+/- [loops::get_elem_mut] -/
+divergent def get_elem_mut_loop_back
+  (x : Usize) (ls : list_t Usize) (ret0 : Usize) : Result (list_t Usize) :=
+  match h: ls with
+  | list_t.Cons y tl =>
+    if y = x
+    then Result.ret (list_t.Cons ret0 tl)
+    else
+      do
+        let tl0 ← get_elem_mut_loop_back x tl ret0
+        Result.ret (list_t.Cons y tl0)
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_back
+  (slots : Vec (list_t Usize)) (x : Usize) (ret0 : Usize) :
+  Result (Vec (list_t Usize))
+  :=
+  do
+    let l ←
+      vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
+    let l0 ← get_elem_mut_loop_back x l ret0
+    vec_index_mut_back (list_t Usize) slots (Usize.ofInt 0 (by intlit)) l0
+
+/- [loops::get_elem_shared] -/
+divergent def get_elem_shared_loop_fwd
+  (x : Usize) (ls : list_t Usize) : Result Usize :=
+  match h: ls with
+  | list_t.Cons y tl =>
+    if y = x
+    then Result.ret y
+    else get_elem_shared_loop_fwd x tl
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_shared] -/
+def get_elem_shared_fwd
+  (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
+  do
+    let l ← vec_index_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
+    get_elem_shared_loop_fwd x l
+
+/- [loops::id_mut] -/
+def id_mut_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
+  Result.ret ls
+
+/- [loops::id_mut] -/
+def id_mut_back
+  (T : Type) (ls : list_t T) (ret0 : list_t T) : Result (list_t T) :=
+  Result.ret ret0
+
+/- [loops::id_shared] -/
+def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
+  Result.ret ls
+
+/- [loops::list_nth_mut_loop_with_id] -/
+divergent def list_nth_mut_loop_with_id_loop_fwd
+  (T : Type) (i : U32) (ls : list_t T) : Result T :=
+  match h: ls with
+  | list_t.Cons x tl =>
+    if i = (U32.ofInt 0 (by intlit))
+    then Result.ret x
+    else
+      do
+        let i0 ← i - (U32.ofInt 1 (by intlit))
+        list_nth_mut_loop_with_id_loop_fwd T i0 tl
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_fwd
+  (T : Type) (ls : list_t T) (i : U32) : Result T :=
+  do
+    let ls0 ← id_mut_fwd T ls
+    list_nth_mut_loop_with_id_loop_fwd T i ls0
+
+/- [loops::list_nth_mut_loop_with_id] -/
+divergent def list_nth_mut_loop_with_id_loop_back
+  (T : Type) (i : U32) (ls : list_t T) (ret0 : T) : Result (list_t T) :=
+  match h: ls with
+  | list_t.Cons x tl =>
+    if i = (U32.ofInt 0 (by intlit))
+    then Result.ret (list_t.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1 (by intlit))
+        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        Result.ret (list_t.Cons x tl0)
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_back
+  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
+  do
+    let ls0 ← id_mut_fwd T ls
+    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
+    id_mut_back T ls l
+
+/- [loops::list_nth_shared_loop_with_id] -/
+divergent def list_nth_shared_loop_with_id_loop_fwd
+  (T : Type) (i : U32) (ls : list_t T) : Result T :=
+  match h: ls with
+  | list_t.Cons x tl =>
+    if i = (U32.ofInt 0 (by intlit))
+    then Result.ret x
+    else
+      do
+        let i0 ← i - (U32.ofInt 1 (by intlit))
+        list_nth_shared_loop_with_id_loop_fwd T i0 tl
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_with_id] -/
+def list_nth_shared_loop_with_id_fwd
+  (T : Type) (ls : list_t T) (i : U32) : Result T :=
+  do
+    let ls0 ← id_shared_fwd T ls
+    list_nth_shared_loop_with_id_loop_fwd T i ls0
+
+/- [loops::list_nth_mut_loop_pair] -/
+divergent def list_nth_mut_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+divergent def list_nth_mut_loop_pair_loop_back'a
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (list_t.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          Result.ret (list_t.Cons x0 tl00)
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_back'a
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_loop_pair] -/
+divergent def list_nth_mut_loop_pair_loop_back'b
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (list_t.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          Result.ret (list_t.Cons x1 tl10)
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_back'b
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair] -/
+divergent def list_nth_shared_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair] -/
+def list_nth_shared_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+divergent def list_nth_mut_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+divergent def list_nth_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
+  Result ((list_t T) × (list_t T))
+  :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then
+        let (t, t0) := ret0
+        Result.ret (list_t.Cons t tl0, list_t.Cons t0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          let (tl00, tl10) ←
+            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (list_t.Cons x0 tl00, list_t.Cons x1 tl10)
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
+  Result ((list_t T) × (list_t T))
+  :=
+  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair_merge] -/
+divergent def list_nth_shared_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair_merge] -/
+def list_nth_shared_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+divergent def list_nth_mut_shared_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+divergent def list_nth_mut_shared_loop_pair_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (list_t.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (list_t.Cons x0 tl00)
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (list_t.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (list_t.Cons x0 tl00)
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+divergent def list_nth_shared_mut_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+divergent def list_nth_shared_mut_loop_pair_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (list_t.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (list_t.Cons x1 tl10)
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
+  list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  match h: ls0 with
+  | list_t.Cons x0 tl0 =>
+    match h: ls1 with
+    | list_t.Cons x1 tl1 =>
+      if i = (U32.ofInt 0 (by intlit))
+      then Result.ret (list_t.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1 (by intlit))
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (list_t.Cons x1 tl10)
+    | list_t.Nil => Result.fail Error.panic
+  | list_t.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
+  Result (list_t T)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+