Reorganize the Lean tests and extract the Polonius tests to Lean

4 files changed, 1168 insertions, 0 deletions

diff --git a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
new file mode 100644
index 00000000..5ddb65ca
--- /dev/null
+++ b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
@@ -0,0 +1,209 @@
+-- [loops]: decreases clauses
+import Base.Primitives
+import Loops.Types
+
+/- [loops::sum]: termination measure -/
+@[simp]
+def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s)
+
+syntax "sum_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::sum_with_mut_borrows]: termination measure -/
+@[simp]
+def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (max, mi, ms)
+
+syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
+
+/- [loops::sum_with_shared_borrows]: termination measure -/
+@[simp]
+def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (max, i, s)
+
+syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::clear]: termination measure -/
+@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i)
+
+syntax "clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
+
+/- [loops::list_mem]: termination measure -/
+@[simp]
+def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls)
+
+syntax "list_mem_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop]: termination measure -/
+@[simp]
+def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32)
+  :=
+  (ls, i)
+
+syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop]: termination measure -/
+@[simp]
+def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T)
+  (i : UInt32) :=
+  (ls, i)
+
+syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::get_elem_mut]: termination measure -/
+@[simp]
+def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_mut_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::get_elem_shared]: termination measure -/
+@[simp]
+def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_shared_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
diff --git a/tests/lean/misc-loops/Loops/Clauses/Template.lean b/tests/lean/misc-loops/Loops/Clauses/Template.lean
new file mode 100644
index 00000000..d1e72d65
--- /dev/null
+++ b/tests/lean/misc-loops/Loops/Clauses/Template.lean
@@ -0,0 +1,210 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: templates for the decreases clauses
+import Base.Primitives
+import Loops.Types
+
+/- [loops::sum]: termination measure -/
+@[simp]
+def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s)
+
+/- [loops::sum]: decreases_by tactic -/
+syntax "sum_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::sum_with_mut_borrows]: termination measure -/
+@[simp]
+def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (max, mi, ms)
+
+/- [loops::sum_with_mut_borrows]: decreases_by tactic -/
+syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
+
+/- [loops::sum_with_shared_borrows]: termination measure -/
+@[simp]
+def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (max, i, s)
+
+/- [loops::sum_with_shared_borrows]: decreases_by tactic -/
+syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::clear]: termination measure -/
+@[simp] def clear_loop_terminates (v : Vec UInt32) (i : USize) := (v, i)
+
+/- [loops::clear]: decreases_by tactic -/
+syntax "clear_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
+
+/- [loops::list_mem]: termination measure -/
+@[simp]
+def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls)
+
+/- [loops::list_mem]: decreases_by tactic -/
+syntax "list_mem_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop]: termination measure -/
+@[simp]
+def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32)
+  :=
+  (ls, i)
+
+/- [loops::list_nth_mut_loop]: decreases_by tactic -/
+syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop]: termination measure -/
+@[simp]
+def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T)
+  (i : UInt32) :=
+  (ls, i)
+
+/- [loops::list_nth_shared_loop]: decreases_by tactic -/
+syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::get_elem_mut]: termination measure -/
+@[simp]
+def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+/- [loops::get_elem_mut]: decreases_by tactic -/
+syntax "get_elem_mut_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::get_elem_shared]: termination measure -/
+@[simp]
+def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+/- [loops::get_elem_shared]: decreases_by tactic -/
+syntax "get_elem_shared_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+/- [loops::list_nth_mut_loop_with_id]: decreases_by tactic -/
+syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+/- [loops::list_nth_shared_loop_with_id]: decreases_by tactic -/
+syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/
+syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/
+syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/
+syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/
+syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/
+syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/
+syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/
+syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/
+syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean
new file mode 100644
index 00000000..5a81ebff
--- /dev/null
+++ b/tests/lean/misc-loops/Loops/Funs.lean
@@ -0,0 +1,740 @@
+-- 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
+
diff --git a/tests/lean/misc-loops/Loops/Types.lean b/tests/lean/misc-loops/Loops/Types.lean
new file mode 100644
index 00000000..f4b6809e
--- /dev/null
+++ b/tests/lean/misc-loops/Loops/Types.lean
@@ -0,0 +1,9 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: type definitions
+import Base.Primitives
+
+/- [loops::List] -/
+inductive list_t (T : Type) :=
+| ListCons : T -> list_t T -> list_t T
+| ListNil : list_t T
+