Merge pull request #44 from AeneasVerif/son_traits_types

Add support for traits

1 files changed, 0 insertions, 612 deletions

diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
deleted file mode 100644
index 5fbe200f..00000000
--- a/tests/lean/Loops/Funs.lean
+++ /dev/null
@@ -1,612 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: function definitions
-import Base
-import Loops.Types
-open Primitives
-
-namespace loops
-
-/- [loops::sum]: loop 0: forward function -/
-divergent def sum_loop (max : U32) (i : U32) (s : U32) : Result U32 :=
-  if i < max
-  then do
-         let s0 ← s + i
-         let i0 ← i + (U32.ofInt 1)
-         sum_loop max i0 s0
-  else s * (U32.ofInt 2)
-
-/- [loops::sum]: forward function -/
-def sum (max : U32) : Result U32 :=
-  sum_loop max (U32.ofInt 0) (U32.ofInt 0)
-
-/- [loops::sum_with_mut_borrows]: loop 0: forward function -/
-divergent def sum_with_mut_borrows_loop
-  (max : U32) (mi : U32) (ms : U32) : Result U32 :=
-  if mi < max
-  then
-    do
-      let ms0 ← ms + mi
-      let mi0 ← mi + (U32.ofInt 1)
-      sum_with_mut_borrows_loop max mi0 ms0
-  else ms * (U32.ofInt 2)
-
-/- [loops::sum_with_mut_borrows]: forward function -/
-def sum_with_mut_borrows (max : U32) : Result U32 :=
-  sum_with_mut_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
-
-/- [loops::sum_with_shared_borrows]: loop 0: forward function -/
-divergent def sum_with_shared_borrows_loop
-  (max : U32) (i : U32) (s : U32) : Result U32 :=
-  if i < max
-  then
-    do
-      let i0 ← i + (U32.ofInt 1)
-      let s0 ← s + i0
-      sum_with_shared_borrows_loop max i0 s0
-  else s * (U32.ofInt 2)
-
-/- [loops::sum_with_shared_borrows]: forward function -/
-def sum_with_shared_borrows (max : U32) : Result U32 :=
-  sum_with_shared_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
-
-/- [loops::clear]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ()) -/
-divergent def clear_loop (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)
-      let v0 ← Vec.index_mut_back U32 v i (U32.ofInt 0)
-      clear_loop v0 i1
-  else Result.ret v
-
-/- [loops::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ()) -/
-def clear (v : Vec U32) : Result (Vec U32) :=
-  clear_loop v (Usize.ofInt 0)
-
-/- [loops::list_mem]: loop 0: forward function -/
-divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
-  match ls with
-  | List.Cons y tl => if y = x
-                      then Result.ret true
-                      else list_mem_loop x tl
-  | List.Nil => Result.ret false
-
-/- [loops::list_mem]: forward function -/
-def list_mem (x : U32) (ls : List U32) : Result Bool :=
-  list_mem_loop x ls
-
-/- [loops::list_nth_mut_loop]: loop 0: forward function -/
-divergent def list_nth_mut_loop_loop
-  (T : Type) (ls : List T) (i : U32) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1)
-           list_nth_mut_loop_loop T tl i0
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop]: forward function -/
-def list_nth_mut_loop (T : Type) (ls : List T) (i : U32) : Result T :=
-  list_nth_mut_loop_loop T ls i
-
-/- [loops::list_nth_mut_loop]: loop 0: backward function 0 -/
-divergent def list_nth_mut_loop_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret (List.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1)
-        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
-        Result.ret (List.Cons x tl0)
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop]: backward function 0 -/
-def list_nth_mut_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
-  list_nth_mut_loop_loop_back T ls i ret0
-
-/- [loops::list_nth_shared_loop]: loop 0: forward function -/
-divergent def list_nth_shared_loop_loop
-  (T : Type) (ls : List T) (i : U32) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1)
-           list_nth_shared_loop_loop T tl i0
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop]: forward function -/
-def list_nth_shared_loop (T : Type) (ls : List T) (i : U32) : Result T :=
-  list_nth_shared_loop_loop T ls i
-
-/- [loops::get_elem_mut]: loop 0: forward function -/
-divergent def get_elem_mut_loop (x : Usize) (ls : List Usize) : Result Usize :=
-  match ls with
-  | List.Cons y tl => if y = x
-                      then Result.ret y
-                      else get_elem_mut_loop x tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::get_elem_mut]: forward function -/
-def get_elem_mut (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
-    get_elem_mut_loop x l
-
-/- [loops::get_elem_mut]: loop 0: backward function 0 -/
-divergent def get_elem_mut_loop_back
-  (x : Usize) (ls : List Usize) (ret0 : Usize) : Result (List Usize) :=
-  match ls with
-  | List.Cons y tl =>
-    if y = x
-    then Result.ret (List.Cons ret0 tl)
-    else
-      do
-        let tl0 ← get_elem_mut_loop_back x tl ret0
-        Result.ret (List.Cons y tl0)
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::get_elem_mut]: backward function 0 -/
-def get_elem_mut_back
-  (slots : Vec (List Usize)) (x : Usize) (ret0 : Usize) :
-  Result (Vec (List Usize))
-  :=
-  do
-    let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
-    let l0 ← get_elem_mut_loop_back x l ret0
-    Vec.index_mut_back (List Usize) slots (Usize.ofInt 0) l0
-
-/- [loops::get_elem_shared]: loop 0: forward function -/
-divergent def get_elem_shared_loop
-  (x : Usize) (ls : List Usize) : Result Usize :=
-  match ls with
-  | List.Cons y tl => if y = x
-                      then Result.ret y
-                      else get_elem_shared_loop x tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::get_elem_shared]: forward function -/
-def get_elem_shared (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ← Vec.index_shared (List Usize) slots (Usize.ofInt 0)
-    get_elem_shared_loop x l
-
-/- [loops::id_mut]: forward function -/
-def id_mut (T : Type) (ls : List T) : Result (List T) :=
-  Result.ret ls
-
-/- [loops::id_mut]: backward function 0 -/
-def id_mut_back (T : Type) (ls : List T) (ret0 : List T) : Result (List T) :=
-  Result.ret ret0
-
-/- [loops::id_shared]: forward function -/
-def id_shared (T : Type) (ls : List T) : Result (List T) :=
-  Result.ret ls
-
-/- [loops::list_nth_mut_loop_with_id]: loop 0: forward function -/
-divergent def list_nth_mut_loop_with_id_loop
-  (T : Type) (i : U32) (ls : List T) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1)
-           list_nth_mut_loop_with_id_loop T i0 tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_with_id]: forward function -/
-def list_nth_mut_loop_with_id (T : Type) (ls : List T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_mut T ls
-    list_nth_mut_loop_with_id_loop T i ls0
-
-/- [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 -/
-divergent def list_nth_mut_loop_with_id_loop_back
-  (T : Type) (i : U32) (ls : List T) (ret0 : T) : Result (List T) :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret (List.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1)
-        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
-        Result.ret (List.Cons x tl0)
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_with_id]: backward function 0 -/
-def list_nth_mut_loop_with_id_back
-  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
-  do
-    let ls0 ← id_mut 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]: loop 0: forward function -/
-divergent def list_nth_shared_loop_with_id_loop
-  (T : Type) (i : U32) (ls : List T) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1)
-        list_nth_shared_loop_with_id_loop T i0 tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop_with_id]: forward function -/
-def list_nth_shared_loop_with_id
-  (T : Type) (ls : List T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_shared T ls
-    list_nth_shared_loop_with_id_loop T i ls0
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: forward function -/
-divergent def list_nth_mut_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair]: forward function -/
-def list_nth_mut_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List 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 -/
-divergent def list_nth_mut_loop_pair_loop_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair]: backward function 0 -/
-def list_nth_mut_loop_pair_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 -/
-divergent def list_nth_mut_loop_pair_loop_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair]: backward function 1 -/
-def list_nth_mut_loop_pair_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair]: loop 0: forward function -/
-divergent def list_nth_shared_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop_pair]: forward function -/
-def list_nth_shared_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_mut_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair_merge]: forward function -/
-def list_nth_mut_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List 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 -/
-divergent def list_nth_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
-  Result ((List T) × (List T))
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then let (t, t0) := ret0
-           Result.ret (List.Cons t tl0, List.Cons t0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let (tl00, tl10) ←
-            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair_merge]: backward function 0 -/
-def list_nth_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
-  Result ((List T) × (List T))
-  :=
-  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_shared_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop_pair_merge]: forward function -/
-def list_nth_shared_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function -/
-divergent def list_nth_mut_shared_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_shared_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair]: forward function -/
-def list_nth_mut_shared_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List 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 -/
-divergent def list_nth_mut_shared_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair]: backward function 0 -/
-def list_nth_mut_shared_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_mut_shared_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function -/
-def list_nth_mut_shared_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List 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 -/
-divergent def list_nth_mut_shared_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 -/
-def list_nth_mut_shared_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function -/
-divergent def list_nth_shared_mut_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_mut_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair]: forward function -/
-def list_nth_shared_mut_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List 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 -/
-divergent def list_nth_shared_mut_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair]: backward function 1 -/
-def list_nth_shared_mut_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_shared_mut_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function -/
-def list_nth_shared_mut_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List 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 -/
-divergent def list_nth_shared_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 -/
-def list_nth_shared_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-end loops