Reorganize the Lean tests and extract the Polonius tests to Lean

1 files changed, 0 insertions, 740 deletions

diff --git a/tests/lean/misc/loops/Loops/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean
deleted file mode 100644
index 5a81ebff..00000000
--- a/tests/lean/misc/loops/Loops/Funs.lean
+++ /dev/null
@@ -1,740 +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 : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) :=
-  if h: i < max
-  then
-    do
-      let s0 ← UInt32.checked_add s i
-      let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
-      sum_loop_fwd max i0 s0
-  else UInt32.checked_mul s (UInt32.ofNatCore 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 : UInt32) : Result UInt32 :=
-  sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
-    (UInt32.ofNatCore 0 (by intlit))
-
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_loop_fwd
-  (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) :=
-  if h: mi < max
-  then
-    do
-      let ms0 ← UInt32.checked_add ms mi
-      let mi0 ← UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
-      sum_with_mut_borrows_loop_fwd max mi0 ms0
-  else UInt32.checked_mul ms (UInt32.ofNatCore 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 : UInt32) : Result UInt32 :=
-  sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
-    (UInt32.ofNatCore 0 (by intlit))
-
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_loop_fwd
-  (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) :=
-  if h: i < max
-  then
-    do
-      let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
-      let s0 ← UInt32.checked_add s i0
-      sum_with_shared_borrows_loop_fwd max i0 s0
-  else UInt32.checked_mul s (UInt32.ofNatCore 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 : UInt32) : Result UInt32 :=
-  sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
-    (UInt32.ofNatCore 0 (by intlit))
-
-/- [loops::clear] -/
-def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) :=
-  let i0 := vec_len UInt32 v
-  if h: i < i0
-  then
-    do
-      let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit))
-      let v0 ← vec_index_mut_back UInt32 v i (UInt32.ofNatCore 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 UInt32) : Result (Vec UInt32) :=
-  clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit))
-
-/- [loops::list_mem] -/
-def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) :=
-  match h: ls with
-  | list_t.ListCons y tl =>
-    if h: y = x
-    then Result.ret true
-    else list_mem_loop_fwd x tl
-  | list_t.ListNil => 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 : UInt32) (ls : list_t UInt32) : 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 : UInt32) : (Result T) :=
-  match h: ls with
-  | list_t.ListCons x tl =>
-    if h: i = (UInt32.ofNatCore 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        list_nth_mut_loop_loop_fwd T tl i0
-  | list_t.ListNil => 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 : UInt32) : 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 : UInt32) (ret0 : T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.ListCons x tl =>
-    if h: i = (UInt32.ofNatCore 0 (by intlit))
-    then Result.ret (list_t.ListCons ret0 tl)
-    else
-      do
-        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
-        Result.ret (list_t.ListCons x tl0)
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) : (Result T) :=
-  match h: ls with
-  | list_t.ListCons x tl =>
-    if h: i = (UInt32.ofNatCore 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        list_nth_shared_loop_loop_fwd T tl i0
-  | list_t.ListNil => 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 : UInt32) : 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.ListCons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_mut_loop_fwd x tl
-  | list_t.ListNil => 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.ofNatCore 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.ListCons y tl =>
-    if h: y = x
-    then Result.ret (list_t.ListCons ret0 tl)
-    else
-      do
-        let tl0 ← get_elem_mut_loop_back x tl ret0
-        Result.ret (list_t.ListCons y tl0)
-  | list_t.ListNil => 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.ofNatCore 0 (by intlit))
-    let l0 ← get_elem_mut_loop_back x l ret0
-    vec_index_mut_back (list_t USize) slots (USize.ofNatCore 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.ListCons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_shared_loop_fwd x tl
-  | list_t.ListNil => 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.ofNatCore 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 : UInt32) (ls : list_t T) : (Result T) :=
-  match h: ls with
-  | list_t.ListCons x tl =>
-    if h: i = (UInt32.ofNatCore 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        list_nth_mut_loop_with_id_loop_fwd T i0 tl
-  | list_t.ListNil => 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 : UInt32) : 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 : UInt32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.ListCons x tl =>
-    if h: i = (UInt32.ofNatCore 0 (by intlit))
-    then Result.ret (list_t.ListCons ret0 tl)
-    else
-      do
-        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
-        Result.ret (list_t.ListCons x tl0)
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) (ls : list_t T) : (Result T) :=
-  match h: ls with
-  | list_t.ListCons x tl =>
-    if h: i = (UInt32.ofNatCore 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        list_nth_shared_loop_with_id_loop_fwd T i0 tl
-  | list_t.ListNil => 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 : UInt32) : 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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (list_t.ListCons ret0 tl0)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
-          Result.ret (list_t.ListCons x0 tl00)
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (list_t.ListCons ret0 tl1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
-          Result.ret (list_t.ListCons x1 tl10)
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) (ret0 : (T × T)) :
-  (Result ((list_t T) × (list_t T)))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then
-        let (t, t0) := ret0
-        Result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let (tl00, tl10) ←
-            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (list_t.ListCons ret0 tl0)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.ListCons x0 tl00)
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (list_t.ListCons ret0 tl0)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.ListCons x0 tl00)
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (list_t.ListCons ret0 tl1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.ListCons x1 tl10)
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
-  (Result (T × T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) :
-  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 : UInt32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.ListCons x0 tl0 =>
-    match h: ls1 with
-    | list_t.ListCons x1 tl1 =>
-      if h: i = (UInt32.ofNatCore 0 (by intlit))
-      then Result.ret (list_t.ListCons ret0 tl1)
-      else
-        do
-          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.ListCons x1 tl10)
-    | list_t.ListNil => Result.fail Error.panic
-  | list_t.ListNil => 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 : UInt32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-