Reorganize the Lean tests

1 files changed, 0 insertions, 705 deletions

diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean
deleted file mode 100644
index fd8d62d7..00000000
--- a/tests/lean/misc-loops/Loops/Funs.lean
+++ /dev/null
@@ -1,705 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: function definitions
-import Base.Primitives
-import Loops.Types
-import Loops.Clauses.Clauses
-
-/- [loops::sum] -/
-def sum_loop_fwd (max : U32) (i : U32) (s : U32) : (Result U32) :=
-  if h: 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))
-termination_by sum_loop_fwd max i s => sum_loop_terminates max i s
-decreasing_by sum_loop_decreases max i s
-
-/- [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] -/
-def sum_with_mut_borrows_loop_fwd
-  (max : U32) (mi : U32) (ms : U32) : (Result U32) :=
-  if h: 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))
-termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
-  sum_with_mut_borrows_loop_terminates max mi ms
-decreasing_by sum_with_mut_borrows_loop_decreases max mi ms
-
-/- [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] -/
-def sum_with_shared_borrows_loop_fwd
-  (max : U32) (i : U32) (s : U32) : (Result U32) :=
-  if h: 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))
-termination_by sum_with_shared_borrows_loop_fwd max i s =>
-  sum_with_shared_borrows_loop_terminates max i s
-decreasing_by sum_with_shared_borrows_loop_decreases max i s
-
-/- [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] -/
-def clear_loop_fwd_back (v : Vec U32) (i : Usize) : (Result (Vec U32)) :=
-  let i0 := vec_len U32 v
-  if h: 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
-termination_by clear_loop_fwd_back v i => clear_loop_terminates v i
-decreasing_by clear_loop_decreases v i
-
-/- [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] -/
-def list_mem_loop_fwd (x : U32) (ls : list_t U32) : (Result Bool) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret true
-    else list_mem_loop_fwd x tl
-  | list_t.Nil => Result.ret false
-termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls
-decreasing_by list_mem_loop_decreases x ls
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_loop_fwd ls i =>
-  list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_loop_back ls i ret0 =>
-  list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_loop_loop_fwd ls i =>
-  list_nth_shared_loop_loop_terminates T ls i
-decreasing_by list_nth_shared_loop_loop_decreases ls i
-
-/- [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] -/
-def get_elem_mut_loop_fwd (x : Usize) (ls : list_t Usize) : (Result Usize) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_mut_loop_fwd x tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [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] -/
-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 h: 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
-termination_by get_elem_mut_loop_back x ls ret0 =>
-  get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [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] -/
-def get_elem_shared_loop_fwd
-  (x : Usize) (ls : list_t Usize) : (Result Usize) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_shared_loop_fwd x tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_shared_loop_fwd x ls =>
-  get_elem_shared_loop_terminates x ls
-decreasing_by get_elem_shared_loop_decreases x ls
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_with_id_loop_fwd i ls =>
-  list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 =>
-  list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_loop_with_id_loop_fwd i ls =>
-  list_nth_shared_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 =>
-  list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [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] -/
-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 h: 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
-termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [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
-