Regenerate the translated files for Lean

9 files changed, 0 insertions, 1873 deletions

diff --git a/tests/lean/betree/Base/Primitives.lean b/tests/lean/betree/Base/Primitives.lean
deleted file mode 100644
index 5b64e908..00000000
--- a/tests/lean/betree/Base/Primitives.lean
+++ /dev/null
@@ -1,392 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
--- USize. They are generally defined in an idiomatic style, except that there is
--- not a single type class to rule them all (more on that below). The absence of
--- type class is intentional, and allows the Lean compiler to efficiently map
--- them to machine integers during compilation.
-
--- USize is designed properly: you cannot reduce `getNumBits` using the
--- simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really
--- support, at least officially, 16-bit microcontrollers, so this seems like a
--- fine design decision for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic|
-    match USize.size, usize_size_eq with
-    | _, Or.inl rfl => decide
-    | _, Or.inr rfl => decide)
-
--- This is how the macro is expected to be used
-#eval USize.ofNatCore 0 (by intlit)
-
--- Also works for other integer types (at the expense of a needless disjunction)
-#eval UInt32.ofNatCore 0 (by intlit)
-
--- The machine integer operations (e.g. sub) are always total, which is not what
--- we want. We therefore define "checked" variants, below. Note that we add a
--- tiny bit of complexity for the USize variant: we first check whether the
--- result is < 2^32; if it is, we can compute the definition, rather than
--- returning a term that is computationally stuck (the comparison to USize.size
--- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def USize.checked_sub (n: USize) (m: USize): Result USize :=
-  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
-  if n >= m then
-    let n' := USize.toNat n
-    let m' := USize.toNat n
-    let r := USize.ofNatCore (n' - m') (by
-      have h: n' - m' <= n' := by
-        apply Nat.sub_le_of_le_add
-        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
-      apply Nat.lt_of_le_of_lt h
-      apply n.val.isLt
-    )
-    return r
-  else
-    fail integerOverflow
-
-@[simp]
-theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
-  match USize.size, usize_size_eq with
-  | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
-  | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
-
-def USize.checked_add (n: USize) (m: USize): Result USize :=
-  if h: n.val + m.val < USize.size then
-    .ret ⟨ n.val + m.val, h ⟩
-  else
-    .fail integerOverflow
-
-def USize.checked_rem (n: USize) (m: USize): Result USize :=
-  if h: m > 0 then
-    .ret ⟨ n.val % m.val, by
-      have h1: ↑m.val < USize.size := m.val.isLt
-      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
-      apply Nat.lt_trans h2 h1
-    ⟩
-  else
-    .fail integerOverflow
-
-def USize.checked_mul (n: USize) (m: USize): Result USize :=
-  if h: n.val * m.val < USize.size then
-    .ret ⟨ n.val * m.val, h ⟩
-  else
-    .fail integerOverflow
-
-def USize.checked_div (n: USize) (m: USize): Result USize :=
-  if m > 0 then
-    .ret ⟨ n.val / m.val, by
-      have h1: ↑n.val < USize.size := n.val.isLt
-      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
-      apply Nat.lt_of_le_of_lt h2 h1
-    ⟩
-  else
-    .fail integerOverflow
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
--- We now define a type class that subsumes the various machine integer types, so
--- as to write a concise definition for scalar_cast, rather than exhaustively
--- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- and fails if a cast operation would involve a truncation or modulo.
-
-class MachineInteger (t: Type) where
-  size: Nat
-  val: t -> Fin size
-  ofNatCore: (n:Nat) -> LT.lt n size -> t
-
-set_option hygiene false in
-run_cmd
-  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
-  Lean.Elab.Command.elabCommand (← `(
-    namespace $typeName
-    instance: MachineInteger $typeName where
-      size := size
-      val := val
-      ofNatCore := ofNatCore
-    end $typeName
-  ))
-
--- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- Lean to infer `src`.
-
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
-  if h: MachineInteger.val x < MachineInteger.size dst then
-    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
-  else
-    .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
--- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
--- rather than maximum values (usize_max).
-def Vec (α : Type u) := { l : List α // List.length l < USize.size }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by {
-  match USize.size, usize_size_eq with
-  | _, Or.inl rfl => simp
-  | _, Or.inr rfl => simp
-  } ⟩
-
-#check vec_new
-
-def vec_len (α : Type u) (v : Vec α) : USize :=
-  let ⟨ v, l ⟩ := v
-  USize.ofNatCore (List.length v) l
-
-#eval vec_len Nat (vec_new Nat)
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
--- NOTE: old version trying to use a subtype notation, but probably better to
--- leave Result elimination to auxiliary lemmas with suitable preconditions
--- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
--- make the proof work in that case? Probably need to import tactics from
--- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
-  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
-  :=
-  if h : List.length v.val + 1 < USize.size then
-    ⟨ return ⟨List.concat v.val x,
-      by
-        rw [List.length_concat]
-        assumption
-     ⟩, by simp ⟩
-  else
-    ⟨ fail maximumSizeExceeded, by simp ⟩
-
-#eval do
-  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
-  -- fields val and property. However, Lean's elaborator can automatically
-  -- select the `val` field if the context provides a type annotation. We
-  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
-  -- side of the monadic let.
-  let v := vec_new Nat
-  let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
-  -- TODO: strengthen post-condition above and do a demo to show that we can
-  -- safely eliminate the `fail` case
-  return (vec_len Nat x)
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val + 1 <= 4294967295 then
-    return ⟨ List.concat v.val x,
-      by
-        rw [List.length_concat]
-        have h': 4294967295 < USize.size := by intlit
-        apply Nat.lt_of_le_of_lt h h'
-    ⟩
-  else if h: List.length v.val + 1 < USize.size then
-    return ⟨List.concat v.val x,
-      by
-        rw [List.length_concat]
-        assumption
-     ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val < USize.size := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
-  if h: i.val < List.length v.val then
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
-  if h: i.val < List.length v.val then
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val < USize.size := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------------
--- SANITY CHECKS --
--------------------
-
--- TODO: add more once we have signed integers
-
-#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/betree/BetreeMain.lean b/tests/lean/betree/BetreeMain.lean
deleted file mode 100644
index 5f307877..00000000
--- a/tests/lean/betree/BetreeMain.lean
+++ /dev/null
@@ -1 +0,0 @@
-import BetreeMain.Funs
diff --git a/tests/lean/betree/BetreeMain/Clauses/Template.lean b/tests/lean/betree/BetreeMain/Clauses/Template.lean
deleted file mode 100644
index 1d18174e..00000000
--- a/tests/lean/betree/BetreeMain/Clauses/Template.lean
+++ /dev/null
@@ -1,185 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [betree_main]: templates for the decreases clauses
-import Base.Primitives
-import BetreeMain.Types
-
-/- [betree_main::betree::List::{1}::len]: termination measure -/
-@[simp]
-def betree_list_len_terminates (T : Type) (self : betree_list_t T) := self
-
-/- [betree_main::betree::List::{1}::len]: decreases_by tactic -/
-syntax "betree_list_len_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_list_len_decreases $self) =>`(tactic| sorry)
-
-/- [betree_main::betree::List::{1}::split_at]: termination measure -/
-@[simp]
-def betree_list_split_at_terminates (T : Type) (self : betree_list_t T)
-  (n : UInt64) :=
-  (self, n)
-
-/- [betree_main::betree::List::{1}::split_at]: decreases_by tactic -/
-syntax "betree_list_split_at_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_list_split_at_decreases $self $n) =>`(tactic| sorry)
-
-/- [betree_main::betree::List::{2}::partition_at_pivot]: termination measure -/
-@[simp]
-def betree_list_partition_at_pivot_terminates (T : Type)
-  (self : betree_list_t (UInt64 × T)) (pivot : UInt64) :=
-  (self, pivot)
-
-/- [betree_main::betree::List::{2}::partition_at_pivot]: decreases_by tactic -/
-syntax "betree_list_partition_at_pivot_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_list_partition_at_pivot_decreases $self $pivot) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::lookup_in_bindings]: termination measure -/
-@[simp]
-def betree_node_lookup_in_bindings_terminates (key : UInt64)
-  (bindings : betree_list_t (UInt64 × UInt64)) :=
-  (key, bindings)
-
-/- [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases_by tactic -/
-syntax "betree_node_lookup_in_bindings_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_lookup_in_bindings_decreases $key $bindings) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: termination measure -/
-@[simp]
-def betree_node_lookup_first_message_for_key_terminates (key : UInt64)
-  (msgs : betree_list_t (UInt64 × betree_message_t)) :=
-  (key, msgs)
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases_by tactic -/
-syntax "betree_node_lookup_first_message_for_key_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_lookup_first_message_for_key_decreases $key $msgs) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::apply_upserts]: termination measure -/
-@[simp]
-def betree_node_apply_upserts_terminates
-  (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64)
-  (key : UInt64) (st : State) :=
-  (msgs, prev, key, st)
-
-/- [betree_main::betree::Node::{5}::apply_upserts]: decreases_by tactic -/
-syntax "betree_node_apply_upserts_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_apply_upserts_decreases $msgs $prev $key $st) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::lookup]: termination measure -/
-@[simp]
-def betree_node_lookup_terminates (self : betree_node_t) (key : UInt64)
-  (st : State) :=
-  (self, key, st)
-
-/- [betree_main::betree::Node::{5}::lookup]: decreases_by tactic -/
-syntax "betree_node_lookup_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_lookup_decreases $self $key $st) =>`(tactic| sorry)
-
-/- [betree_main::betree::Internal::{4}::lookup_in_children]: termination measure -/
-@[simp]
-def betree_internal_lookup_in_children_terminates (self : betree_internal_t)
-  (key : UInt64) (st : State) :=
-  (self, key, st)
-
-/- [betree_main::betree::Internal::{4}::lookup_in_children]: decreases_by tactic -/
-syntax "betree_internal_lookup_in_children_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_internal_lookup_in_children_decreases $self $key $st) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: termination measure -/
-@[simp]
-def betree_node_lookup_mut_in_bindings_terminates (key : UInt64)
-  (bindings : betree_list_t (UInt64 × UInt64)) :=
-  (key, bindings)
-
-/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases_by tactic -/
-syntax "betree_node_lookup_mut_in_bindings_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_lookup_mut_in_bindings_decreases $key $bindings) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::apply_messages_to_leaf]: termination measure -/
-@[simp]
-def betree_node_apply_messages_to_leaf_terminates
-  (bindings : betree_list_t (UInt64 × UInt64))
-  (new_msgs : betree_list_t (UInt64 × betree_message_t)) :=
-  (bindings, new_msgs)
-
-/- [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases_by tactic -/
-syntax "betree_node_apply_messages_to_leaf_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_apply_messages_to_leaf_decreases $bindings
-$new_msgs) =>`(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::filter_messages_for_key]: termination measure -/
-@[simp]
-def betree_node_filter_messages_for_key_terminates (key : UInt64)
-  (msgs : betree_list_t (UInt64 × betree_message_t)) :=
-  (key, msgs)
-
-/- [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases_by tactic -/
-syntax "betree_node_filter_messages_for_key_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_filter_messages_for_key_decreases $key $msgs) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: termination measure -/
-@[simp]
-def betree_node_lookup_first_message_after_key_terminates (key : UInt64)
-  (msgs : betree_list_t (UInt64 × betree_message_t)) :=
-  (key, msgs)
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases_by tactic -/
-syntax "betree_node_lookup_first_message_after_key_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_lookup_first_message_after_key_decreases $key $msgs) =>
-  `(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::apply_messages_to_internal]: termination measure -/
-@[simp]
-def betree_node_apply_messages_to_internal_terminates
-  (msgs : betree_list_t (UInt64 × betree_message_t))
-  (new_msgs : betree_list_t (UInt64 × betree_message_t)) :=
-  (msgs, new_msgs)
-
-/- [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases_by tactic -/
-syntax "betree_node_apply_messages_to_internal_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_apply_messages_to_internal_decreases $msgs
-$new_msgs) =>`(tactic| sorry)
-
-/- [betree_main::betree::Node::{5}::apply_messages]: termination measure -/
-@[simp]
-def betree_node_apply_messages_terminates (self : betree_node_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) :=
-  (self, params, node_id_cnt, msgs, st)
-
-/- [betree_main::betree::Node::{5}::apply_messages]: decreases_by tactic -/
-syntax "betree_node_apply_messages_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_node_apply_messages_decreases $self $params $node_id_cnt
-$msgs $st) =>`(tactic| sorry)
-
-/- [betree_main::betree::Internal::{4}::flush]: termination measure -/
-@[simp]
-def betree_internal_flush_terminates (self : betree_internal_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (UInt64 × betree_message_t)) (st : State) :=
-  (self, params, node_id_cnt, content, st)
-
-/- [betree_main::betree::Internal::{4}::flush]: decreases_by tactic -/
-syntax "betree_internal_flush_decreases" term+ : tactic
-macro_rules
-| `(tactic| betree_internal_flush_decreases $self $params $node_id_cnt $content
-$st) =>`(tactic| sorry)
-
diff --git a/tests/lean/betree/BetreeMain/Funs.lean b/tests/lean/betree/BetreeMain/Funs.lean
deleted file mode 100644
index 7177e2ec..00000000
--- a/tests/lean/betree/BetreeMain/Funs.lean
+++ /dev/null
@@ -1,1167 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [betree_main]: function definitions
-import Base.Primitives
-import BetreeMain.Types
-import BetreeMain.Opaque
-import BetreeMain.Clauses.Clauses
-
-section variable (opaque_defs: OpaqueDefs)
-
-/- [betree_main::betree::load_internal_node] -/
-def betree_load_internal_node_fwd
-  (id : UInt64) (st : State) :
-  Result (State × (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  opaque_defs.betree_utils_load_internal_node_fwd id st
-
-/- [betree_main::betree::store_internal_node] -/
-def betree_store_internal_node_fwd
-  (id : UInt64) (content : betree_list_t (UInt64 × betree_message_t))
-  (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      opaque_defs.betree_utils_store_internal_node_fwd id content st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::load_leaf_node] -/
-def betree_load_leaf_node_fwd
-  (id : UInt64) (st : State) :
-  Result (State × (betree_list_t (UInt64 × UInt64)))
-  :=
-  opaque_defs.betree_utils_load_leaf_node_fwd id st
-
-/- [betree_main::betree::store_leaf_node] -/
-def betree_store_leaf_node_fwd
-  (id : UInt64) (content : betree_list_t (UInt64 × UInt64)) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ← opaque_defs.betree_utils_store_leaf_node_fwd id content st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::fresh_node_id] -/
-def betree_fresh_node_id_fwd (counter : UInt64) : Result UInt64 :=
-  do
-    let _ ← UInt64.checked_add counter (UInt64.ofNatCore 1 (by intlit))
-    Result.ret counter
-
-/- [betree_main::betree::fresh_node_id] -/
-def betree_fresh_node_id_back (counter : UInt64) : Result UInt64 :=
-  UInt64.checked_add counter (UInt64.ofNatCore 1 (by intlit))
-
-/- [betree_main::betree::NodeIdCounter::{0}::new] -/
-def betree_node_id_counter_new_fwd : Result betree_node_id_counter_t :=
-  Result.ret
-  { betree_node_id_counter_next_node_id := (UInt64.ofNatCore 0 (by intlit)) }
-
-/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/
-def betree_node_id_counter_fresh_id_fwd
-  (self : betree_node_id_counter_t) : Result UInt64 :=
-  do
-    let _ ← UInt64.checked_add self.betree_node_id_counter_next_node_id
-      (UInt64.ofNatCore 1 (by intlit))
-    Result.ret self.betree_node_id_counter_next_node_id
-
-/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/
-def betree_node_id_counter_fresh_id_back
-  (self : betree_node_id_counter_t) : Result betree_node_id_counter_t :=
-  do
-    let i ← UInt64.checked_add self.betree_node_id_counter_next_node_id
-      (UInt64.ofNatCore 1 (by intlit))
-    Result.ret { betree_node_id_counter_next_node_id := i }
-
-/- [core::num::u64::{10}::MAX] -/
-def core_num_u64_max_body : Result UInt64 :=
-  Result.ret (UInt64.ofNatCore 18446744073709551615 (by intlit))
-def core_num_u64_max_c : UInt64 := eval_global core_num_u64_max_body (by simp)
-
-/- [betree_main::betree::upsert_update] -/
-def betree_upsert_update_fwd
-  (prev : Option UInt64) (st : betree_upsert_fun_state_t) : Result UInt64 :=
-  match h: prev with
-  | Option.none =>
-    match h: st with
-    | betree_upsert_fun_state_t.Add v => Result.ret v
-    | betree_upsert_fun_state_t.Sub i =>
-      Result.ret (UInt64.ofNatCore 0 (by intlit))
-  | Option.some prev0 =>
-    match h: st with
-    | betree_upsert_fun_state_t.Add v =>
-      do
-        let margin ← UInt64.checked_sub core_num_u64_max_c prev0
-        if h: margin >= v
-        then UInt64.checked_add prev0 v
-        else Result.ret core_num_u64_max_c
-    | betree_upsert_fun_state_t.Sub v =>
-      if h: prev0 >= v
-      then UInt64.checked_sub prev0 v
-      else Result.ret (UInt64.ofNatCore 0 (by intlit))
-
-/- [betree_main::betree::List::{1}::len] -/
-def betree_list_len_fwd
-  (T : Type) (self : betree_list_t T) : (Result UInt64) :=
-  match h: self with
-  | betree_list_t.Cons t tl =>
-    do
-      let i ← betree_list_len_fwd T tl
-      UInt64.checked_add (UInt64.ofNatCore 1 (by intlit)) i
-  | betree_list_t.Nil => Result.ret (UInt64.ofNatCore 0 (by intlit))
-termination_by betree_list_len_fwd self => betree_list_len_terminates T self
-decreasing_by betree_list_len_decreases self
-
-/- [betree_main::betree::List::{1}::split_at] -/
-def betree_list_split_at_fwd
-  (T : Type) (self : betree_list_t T) (n : UInt64) :
-  (Result ((betree_list_t T) × (betree_list_t T)))
-  :=
-  if h: n = (UInt64.ofNatCore 0 (by intlit))
-  then Result.ret (betree_list_t.Nil, self)
-  else
-    match h: self with
-    | betree_list_t.Cons hd tl =>
-      do
-        let i ← UInt64.checked_sub n (UInt64.ofNatCore 1 (by intlit))
-        let p ← betree_list_split_at_fwd T tl i
-        let (ls0, ls1) := p
-        let l := ls0
-        Result.ret (betree_list_t.Cons hd l, ls1)
-    | betree_list_t.Nil => Result.fail Error.panic
-termination_by betree_list_split_at_fwd self n =>
-  betree_list_split_at_terminates T self n
-decreasing_by betree_list_split_at_decreases self n
-
-/- [betree_main::betree::List::{1}::push_front] -/
-def betree_list_push_front_fwd_back
-  (T : Type) (self : betree_list_t T) (x : T) : Result (betree_list_t T) :=
-  let tl := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
-  let l := tl
-  Result.ret (betree_list_t.Cons x l)
-
-/- [betree_main::betree::List::{1}::pop_front] -/
-def betree_list_pop_front_fwd (T : Type) (self : betree_list_t T) : Result T :=
-  let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
-  match h: ls with
-  | betree_list_t.Cons x tl => Result.ret x
-  | betree_list_t.Nil => Result.fail Error.panic
-
-/- [betree_main::betree::List::{1}::pop_front] -/
-def betree_list_pop_front_back
-  (T : Type) (self : betree_list_t T) : Result (betree_list_t T) :=
-  let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
-  match h: ls with
-  | betree_list_t.Cons x tl => Result.ret tl
-  | betree_list_t.Nil => Result.fail Error.panic
-
-/- [betree_main::betree::List::{1}::hd] -/
-def betree_list_hd_fwd (T : Type) (self : betree_list_t T) : Result T :=
-  match h: self with
-  | betree_list_t.Cons hd l => Result.ret hd
-  | betree_list_t.Nil => Result.fail Error.panic
-
-/- [betree_main::betree::List::{2}::head_has_key] -/
-def betree_list_head_has_key_fwd
-  (T : Type) (self : betree_list_t (UInt64 × T)) (key : UInt64) :
-  Result Bool
-  :=
-  match h: self with
-  | betree_list_t.Cons hd l => let (i, _) := hd
-                               Result.ret (i = key)
-  | betree_list_t.Nil => Result.ret false
-
-/- [betree_main::betree::List::{2}::partition_at_pivot] -/
-def betree_list_partition_at_pivot_fwd
-  (T : Type) (self : betree_list_t (UInt64 × T)) (pivot : UInt64) :
-  (Result ((betree_list_t (UInt64 × T)) × (betree_list_t (UInt64 × T))))
-  :=
-  match h: self with
-  | betree_list_t.Cons hd tl =>
-    let (i, t) := hd
-    if h: i >= pivot
-    then Result.ret (betree_list_t.Nil, betree_list_t.Cons (i, t) tl)
-    else
-      do
-        let p ← betree_list_partition_at_pivot_fwd T tl pivot
-        let (ls0, ls1) := p
-        let l := ls0
-        Result.ret (betree_list_t.Cons (i, t) l, ls1)
-  | betree_list_t.Nil => Result.ret (betree_list_t.Nil, betree_list_t.Nil)
-termination_by betree_list_partition_at_pivot_fwd self pivot =>
-  betree_list_partition_at_pivot_terminates T self pivot
-decreasing_by betree_list_partition_at_pivot_decreases self pivot
-
-/- [betree_main::betree::Leaf::{3}::split] -/
-def betree_leaf_split_fwd
-  (self : betree_leaf_t) (content : betree_list_t (UInt64 × UInt64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (st : State) :
-  Result (State × betree_internal_t)
-  :=
-  do
-    let p ←
-      betree_list_split_at_fwd (UInt64 × UInt64) content
-        params.betree_params_split_size
-    let (content0, content1) := p
-    let p0 ← betree_list_hd_fwd (UInt64 × UInt64) content1
-    let (pivot, _) := p0
-    let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt
-    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
-    let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0
-    let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st
-    let (st1, _) ← betree_store_leaf_node_fwd id1 content1 st0
-    let n := betree_node_t.Leaf
-      {
-        betree_leaf_id := id0,
-        betree_leaf_size := params.betree_params_split_size
-      }
-    let n0 := betree_node_t.Leaf
-      {
-        betree_leaf_id := id1,
-        betree_leaf_size := params.betree_params_split_size
-      }
-    Result.ret (st1, mkbetree_internal_t self.betree_leaf_id pivot n n0)
-
-/- [betree_main::betree::Leaf::{3}::split] -/
-def betree_leaf_split_back
-  (self : betree_leaf_t) (content : betree_list_t (UInt64 × UInt64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (st : State) :
-  Result betree_node_id_counter_t
-  :=
-  do
-    let p ←
-      betree_list_split_at_fwd (UInt64 × UInt64) content
-        params.betree_params_split_size
-    let (content0, content1) := p
-    let _ ← betree_list_hd_fwd (UInt64 × UInt64) content1
-    let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt
-    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
-    let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0
-    let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st
-    let _ ← betree_store_leaf_node_fwd id1 content1 st0
-    betree_node_id_counter_fresh_id_back node_id_cnt0
-
-/- [betree_main::betree::Node::{5}::lookup_in_bindings] -/
-def betree_node_lookup_in_bindings_fwd
-  (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) :
-  (Result (Option UInt64))
-  :=
-  match h: bindings with
-  | betree_list_t.Cons hd tl =>
-    let (i, i0) := hd
-    if h: i = key
-    then Result.ret (Option.some i0)
-    else
-      if h: i > key
-      then Result.ret Option.none
-      else betree_node_lookup_in_bindings_fwd key tl
-  | betree_list_t.Nil => Result.ret Option.none
-termination_by betree_node_lookup_in_bindings_fwd key bindings =>
-  betree_node_lookup_in_bindings_terminates key bindings
-decreasing_by betree_node_lookup_in_bindings_decreases key bindings
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/
-def betree_node_lookup_first_message_for_key_fwd
-  (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) :
-  (Result (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  match h: msgs with
-  | betree_list_t.Cons x next_msgs =>
-    let (i, m) := x
-    if h: i >= key
-    then Result.ret (betree_list_t.Cons (i, m) next_msgs)
-    else betree_node_lookup_first_message_for_key_fwd key next_msgs
-  | betree_list_t.Nil => Result.ret betree_list_t.Nil
-termination_by betree_node_lookup_first_message_for_key_fwd key msgs =>
-  betree_node_lookup_first_message_for_key_terminates key msgs
-decreasing_by betree_node_lookup_first_message_for_key_decreases key msgs
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/
-def betree_node_lookup_first_message_for_key_back
-  (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t))
-  (ret0 : betree_list_t (UInt64 × betree_message_t)) :
-  (Result (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  match h: msgs with
-  | betree_list_t.Cons x next_msgs =>
-    let (i, m) := x
-    if h: i >= key
-    then Result.ret ret0
-    else
-      do
-        let next_msgs0 ←
-          betree_node_lookup_first_message_for_key_back key next_msgs ret0
-        Result.ret (betree_list_t.Cons (i, m) next_msgs0)
-  | betree_list_t.Nil => Result.ret ret0
-termination_by betree_node_lookup_first_message_for_key_back key msgs ret0 =>
-  betree_node_lookup_first_message_for_key_terminates key msgs
-decreasing_by betree_node_lookup_first_message_for_key_decreases key msgs
-
-/- [betree_main::betree::Node::{5}::apply_upserts] -/
-def betree_node_apply_upserts_fwd
-  (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64)
-  (key : UInt64) (st : State) :
-  (Result (State × UInt64))
-  :=
-  do
-    let b ← betree_list_head_has_key_fwd betree_message_t msgs key
-    if h: b
-    then
-      do
-        let msg ← betree_list_pop_front_fwd (UInt64 × betree_message_t) msgs
-        let (_, m) := msg
-        match h: m with
-        | betree_message_t.Insert i => Result.fail Error.panic
-        | betree_message_t.Delete => Result.fail Error.panic
-        | betree_message_t.Upsert s =>
-          do
-            let v ← betree_upsert_update_fwd prev s
-            let msgs0 ←
-              betree_list_pop_front_back (UInt64 × betree_message_t) msgs
-            betree_node_apply_upserts_fwd msgs0 (Option.some v) key st
-    else
-      do
-        let (st0, v) ←
-          opaque_defs.core_option_option_unwrap_fwd UInt64 prev st
-        let _ ←
-          betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs
-            (key, betree_message_t.Insert v)
-        Result.ret (st0, v)
-termination_by betree_node_apply_upserts_fwd msgs prev key st =>
-  betree_node_apply_upserts_terminates msgs prev key st
-decreasing_by betree_node_apply_upserts_decreases msgs prev key st
-
-/- [betree_main::betree::Node::{5}::apply_upserts] -/
-def betree_node_apply_upserts_back
-  (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64)
-  (key : UInt64) (st : State) :
-  (Result (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  do
-    let b ← betree_list_head_has_key_fwd betree_message_t msgs key
-    if h: b
-    then
-      do
-        let msg ← betree_list_pop_front_fwd (UInt64 × betree_message_t) msgs
-        let (_, m) := msg
-        match h: m with
-        | betree_message_t.Insert i => Result.fail Error.panic
-        | betree_message_t.Delete => Result.fail Error.panic
-        | betree_message_t.Upsert s =>
-          do
-            let v ← betree_upsert_update_fwd prev s
-            let msgs0 ←
-              betree_list_pop_front_back (UInt64 × betree_message_t) msgs
-            betree_node_apply_upserts_back msgs0 (Option.some v) key st
-    else
-      do
-        let (_, v) ← opaque_defs.core_option_option_unwrap_fwd UInt64 prev st
-        betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs (key,
-          betree_message_t.Insert v)
-termination_by betree_node_apply_upserts_back msgs prev key st =>
-  betree_node_apply_upserts_terminates msgs prev key st
-decreasing_by betree_node_apply_upserts_decreases msgs prev key st
-
-/- [betree_main::betree::Node::{5}::lookup] -/
-mutual def betree_node_lookup_fwd
-  (self : betree_node_t) (key : UInt64) (st : State) :
-  (Result (State × (Option UInt64)))
-  :=
-  match h: self with
-  | betree_node_t.Internal node =>
-    do
-      let (mkbetree_internal_t i i0 n n0) := node
-      let (st0, msgs) ← betree_load_internal_node_fwd i st
-      let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
-      match h: pending with
-      | betree_list_t.Cons p l =>
-        let (k, msg) := p
-        if h: k != key
-        then
-          do
-            let (st1, opt) ←
-              betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0
-                n n0) key st0
-            let _ ←
-              betree_node_lookup_first_message_for_key_back key msgs
-                (betree_list_t.Cons (k, msg) l)
-            Result.ret (st1, opt)
-        else
-          match h: msg with
-          | betree_message_t.Insert v =>
-            do
-              let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
-                  (betree_list_t.Cons (k, betree_message_t.Insert v) l)
-              Result.ret (st0, Option.some v)
-          | betree_message_t.Delete =>
-            do
-              let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
-                  (betree_list_t.Cons (k, betree_message_t.Delete) l)
-              Result.ret (st0, Option.none)
-          | betree_message_t.Upsert ufs =>
-            do
-              let (st1, v) ←
-                betree_internal_lookup_in_children_fwd (mkbetree_internal_t i
-                  i0 n n0) key st0
-              let (st2, v0) ←
-                betree_node_apply_upserts_fwd (betree_list_t.Cons (k,
-                  betree_message_t.Upsert ufs) l) v key st1
-              let node0 ←
-                betree_internal_lookup_in_children_back (mkbetree_internal_t i
-                  i0 n n0) key st0
-              let (mkbetree_internal_t i1 _ _ _) := node0
-              let pending0 ←
-                betree_node_apply_upserts_back (betree_list_t.Cons (k,
-                  betree_message_t.Upsert ufs) l) v key st1
-              let msgs0 ←
-                betree_node_lookup_first_message_for_key_back key msgs pending0
-              let (st3, _) ← betree_store_internal_node_fwd i1 msgs0 st2
-              Result.ret (st3, Option.some v0)
-      | betree_list_t.Nil =>
-        do
-          let (st1, opt) ←
-            betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0 n
-              n0) key st0
-          let _ ←
-            betree_node_lookup_first_message_for_key_back key msgs
-              betree_list_t.Nil
-          Result.ret (st1, opt)
-  | betree_node_t.Leaf node =>
-    do
-      let (st0, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let opt ← betree_node_lookup_in_bindings_fwd key bindings
-      Result.ret (st0, opt)
-termination_by betree_node_lookup_fwd self key st =>
-  betree_node_lookup_terminates self key st
-decreasing_by betree_node_lookup_decreases self key st
-
-/- [betree_main::betree::Node::{5}::lookup] -/
-def betree_node_lookup_back
-  (self : betree_node_t) (key : UInt64) (st : State) :
-  (Result betree_node_t)
-  :=
-  match h: self with
-  | betree_node_t.Internal node =>
-    do
-      let (mkbetree_internal_t i i0 n n0) := node
-      let (st0, msgs) ← betree_load_internal_node_fwd i st
-      let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
-      match h: pending with
-      | betree_list_t.Cons p l =>
-        let (k, msg) := p
-        if h: k != key
-        then
-          do
-            let _ ←
-              betree_node_lookup_first_message_for_key_back key msgs
-                (betree_list_t.Cons (k, msg) l)
-            let node0 ←
-              betree_internal_lookup_in_children_back (mkbetree_internal_t i i0
-                n n0) key st0
-            Result.ret (betree_node_t.Internal node0)
-        else
-          match h: msg with
-          | betree_message_t.Insert v =>
-            do
-              let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
-                  (betree_list_t.Cons (k, betree_message_t.Insert v) l)
-              Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n
-                n0))
-          | betree_message_t.Delete =>
-            do
-              let _ ←
-                betree_node_lookup_first_message_for_key_back key msgs
-                  (betree_list_t.Cons (k, betree_message_t.Delete) l)
-              Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n
-                n0))
-          | betree_message_t.Upsert ufs =>
-            do
-              let (st1, v) ←
-                betree_internal_lookup_in_children_fwd (mkbetree_internal_t i
-                  i0 n n0) key st0
-              let (st2, _) ←
-                betree_node_apply_upserts_fwd (betree_list_t.Cons (k,
-                  betree_message_t.Upsert ufs) l) v key st1
-              let node0 ←
-                betree_internal_lookup_in_children_back (mkbetree_internal_t i
-                  i0 n n0) key st0
-              let (mkbetree_internal_t i1 i2 n1 n2) := node0
-              let pending0 ←
-                betree_node_apply_upserts_back (betree_list_t.Cons (k,
-                  betree_message_t.Upsert ufs) l) v key st1
-              let msgs0 ←
-                betree_node_lookup_first_message_for_key_back key msgs pending0
-              let _ ← betree_store_internal_node_fwd i1 msgs0 st2
-              Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1
-                n2))
-      | betree_list_t.Nil =>
-        do
-          let _ ←
-            betree_node_lookup_first_message_for_key_back key msgs
-              betree_list_t.Nil
-          let node0 ←
-            betree_internal_lookup_in_children_back (mkbetree_internal_t i i0 n
-              n0) key st0
-          Result.ret (betree_node_t.Internal node0)
-  | betree_node_t.Leaf node =>
-    do
-      let (_, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let _ ← betree_node_lookup_in_bindings_fwd key bindings
-      Result.ret (betree_node_t.Leaf node)
-termination_by betree_node_lookup_back self key st =>
-  betree_node_lookup_terminates self key st
-decreasing_by betree_node_lookup_decreases self key st
-
-/- [betree_main::betree::Internal::{4}::lookup_in_children] -/
-def betree_internal_lookup_in_children_fwd
-  (self : betree_internal_t) (key : UInt64) (st : State) :
-  (Result (State × (Option UInt64)))
-  :=
-  let (mkbetree_internal_t _ i n n0) := self
-  if h: key < i
-  then betree_node_lookup_fwd n key st
-  else betree_node_lookup_fwd n0 key st
-termination_by betree_internal_lookup_in_children_fwd self key st =>
-  betree_internal_lookup_in_children_terminates self key st
-decreasing_by betree_internal_lookup_in_children_decreases self key st
-
-/- [betree_main::betree::Internal::{4}::lookup_in_children] -/
-def betree_internal_lookup_in_children_back
-  (self : betree_internal_t) (key : UInt64) (st : State) :
-  (Result betree_internal_t)
-  :=
-  let (mkbetree_internal_t i i0 n n0) := self
-  if h: key < i0
-  then
-    do
-      let n1 ← betree_node_lookup_back n key st
-      Result.ret (mkbetree_internal_t i i0 n1 n0)
-  else
-    do
-      let n1 ← betree_node_lookup_back n0 key st
-      Result.ret (mkbetree_internal_t i i0 n n1)
-termination_by betree_internal_lookup_in_children_back self key st =>
-  betree_internal_lookup_in_children_terminates self key st
-decreasing_by betree_internal_lookup_in_children_decreases self key st
-
-/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
-def betree_node_lookup_mut_in_bindings_fwd
-  (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) :
-  (Result (betree_list_t (UInt64 × UInt64)))
-  :=
-  match h: bindings with
-  | betree_list_t.Cons hd tl =>
-    let (i, i0) := hd
-    if h: i >= key
-    then Result.ret (betree_list_t.Cons (i, i0) tl)
-    else betree_node_lookup_mut_in_bindings_fwd key tl
-  | betree_list_t.Nil => Result.ret betree_list_t.Nil
-termination_by betree_node_lookup_mut_in_bindings_fwd key bindings =>
-  betree_node_lookup_mut_in_bindings_terminates key bindings
-decreasing_by betree_node_lookup_mut_in_bindings_decreases key bindings
-
-/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
-def betree_node_lookup_mut_in_bindings_back
-  (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64))
-  (ret0 : betree_list_t (UInt64 × UInt64)) :
-  (Result (betree_list_t (UInt64 × UInt64)))
-  :=
-  match h: bindings with
-  | betree_list_t.Cons hd tl =>
-    let (i, i0) := hd
-    if h: i >= key
-    then Result.ret ret0
-    else
-      do
-        let tl0 ← betree_node_lookup_mut_in_bindings_back key tl ret0
-        Result.ret (betree_list_t.Cons (i, i0) tl0)
-  | betree_list_t.Nil => Result.ret ret0
-termination_by betree_node_lookup_mut_in_bindings_back key bindings ret0 =>
-  betree_node_lookup_mut_in_bindings_terminates key bindings
-decreasing_by betree_node_lookup_mut_in_bindings_decreases key bindings
-
-/- [betree_main::betree::Node::{5}::apply_to_leaf] -/
-def betree_node_apply_to_leaf_fwd_back
-  (bindings : betree_list_t (UInt64 × UInt64)) (key : UInt64)
-  (new_msg : betree_message_t) :
-  Result (betree_list_t (UInt64 × UInt64))
-  :=
-  do
-    let bindings0 ← betree_node_lookup_mut_in_bindings_fwd key bindings
-    let b ← betree_list_head_has_key_fwd UInt64 bindings0 key
-    if h: b
-    then
-      do
-        let hd ← betree_list_pop_front_fwd (UInt64 × UInt64) bindings0
-        match h: new_msg with
-        | betree_message_t.Insert v =>
-          do
-            let bindings1 ←
-              betree_list_pop_front_back (UInt64 × UInt64) bindings0
-            let bindings2 ←
-              betree_list_push_front_fwd_back (UInt64 × UInt64) bindings1
-                (key, v)
-            betree_node_lookup_mut_in_bindings_back key bindings bindings2
-        | betree_message_t.Delete =>
-          do
-            let bindings1 ←
-              betree_list_pop_front_back (UInt64 × UInt64) bindings0
-            betree_node_lookup_mut_in_bindings_back key bindings bindings1
-        | betree_message_t.Upsert s =>
-          do
-            let (_, i) := hd
-            let v ← betree_upsert_update_fwd (Option.some i) s
-            let bindings1 ←
-              betree_list_pop_front_back (UInt64 × UInt64) bindings0
-            let bindings2 ←
-              betree_list_push_front_fwd_back (UInt64 × UInt64) bindings1
-                (key, v)
-            betree_node_lookup_mut_in_bindings_back key bindings bindings2
-    else
-      match h: new_msg with
-      | betree_message_t.Insert v =>
-        do
-          let bindings1 ←
-            betree_list_push_front_fwd_back (UInt64 × UInt64) bindings0 (key,
-              v)
-          betree_node_lookup_mut_in_bindings_back key bindings bindings1
-      | betree_message_t.Delete =>
-        betree_node_lookup_mut_in_bindings_back key bindings bindings0
-      | betree_message_t.Upsert s =>
-        do
-          let v ← betree_upsert_update_fwd Option.none s
-          let bindings1 ←
-            betree_list_push_front_fwd_back (UInt64 × UInt64) bindings0 (key,
-              v)
-          betree_node_lookup_mut_in_bindings_back key bindings bindings1
-
-/- [betree_main::betree::Node::{5}::apply_messages_to_leaf] -/
-def betree_node_apply_messages_to_leaf_fwd_back
-  (bindings : betree_list_t (UInt64 × UInt64))
-  (new_msgs : betree_list_t (UInt64 × betree_message_t)) :
-  (Result (betree_list_t (UInt64 × UInt64)))
-  :=
-  match h: new_msgs with
-  | betree_list_t.Cons new_msg new_msgs_tl =>
-    do
-      let (i, m) := new_msg
-      let bindings0 ← betree_node_apply_to_leaf_fwd_back bindings i m
-      betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
-  | betree_list_t.Nil => Result.ret bindings
-termination_by betree_node_apply_messages_to_leaf_fwd_back bindings new_msgs =>
-  betree_node_apply_messages_to_leaf_terminates bindings new_msgs
-decreasing_by betree_node_apply_messages_to_leaf_decreases bindings new_msgs
-
-/- [betree_main::betree::Node::{5}::filter_messages_for_key] -/
-def betree_node_filter_messages_for_key_fwd_back
-  (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) :
-  (Result (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  match h: msgs with
-  | betree_list_t.Cons p l =>
-    let (k, m) := p
-    if h: k = key
-    then
-      do
-        let msgs0 ←
-          betree_list_pop_front_back (UInt64 × betree_message_t)
-            (betree_list_t.Cons (k, m) l)
-        betree_node_filter_messages_for_key_fwd_back key msgs0
-    else Result.ret (betree_list_t.Cons (k, m) l)
-  | betree_list_t.Nil => Result.ret betree_list_t.Nil
-termination_by betree_node_filter_messages_for_key_fwd_back key msgs =>
-  betree_node_filter_messages_for_key_terminates key msgs
-decreasing_by betree_node_filter_messages_for_key_decreases key msgs
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
-def betree_node_lookup_first_message_after_key_fwd
-  (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) :
-  (Result (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  match h: msgs with
-  | betree_list_t.Cons p next_msgs =>
-    let (k, m) := p
-    if h: k = key
-    then betree_node_lookup_first_message_after_key_fwd key next_msgs
-    else Result.ret (betree_list_t.Cons (k, m) next_msgs)
-  | betree_list_t.Nil => Result.ret betree_list_t.Nil
-termination_by betree_node_lookup_first_message_after_key_fwd key msgs =>
-  betree_node_lookup_first_message_after_key_terminates key msgs
-decreasing_by betree_node_lookup_first_message_after_key_decreases key msgs
-
-/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
-def betree_node_lookup_first_message_after_key_back
-  (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t))
-  (ret0 : betree_list_t (UInt64 × betree_message_t)) :
-  (Result (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  match h: msgs with
-  | betree_list_t.Cons p next_msgs =>
-    let (k, m) := p
-    if h: k = key
-    then
-      do
-        let next_msgs0 ←
-          betree_node_lookup_first_message_after_key_back key next_msgs ret0
-        Result.ret (betree_list_t.Cons (k, m) next_msgs0)
-    else Result.ret ret0
-  | betree_list_t.Nil => Result.ret ret0
-termination_by betree_node_lookup_first_message_after_key_back key msgs ret0 =>
-  betree_node_lookup_first_message_after_key_terminates key msgs
-decreasing_by betree_node_lookup_first_message_after_key_decreases key msgs
-
-/- [betree_main::betree::Node::{5}::apply_to_internal] -/
-def betree_node_apply_to_internal_fwd_back
-  (msgs : betree_list_t (UInt64 × betree_message_t)) (key : UInt64)
-  (new_msg : betree_message_t) :
-  Result (betree_list_t (UInt64 × betree_message_t))
-  :=
-  do
-    let msgs0 ← betree_node_lookup_first_message_for_key_fwd key msgs
-    let b ← betree_list_head_has_key_fwd betree_message_t msgs0 key
-    if h: b
-    then
-      match h: new_msg with
-      | betree_message_t.Insert i =>
-        do
-          let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0
-          let msgs2 ←
-            betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs1
-              (key, betree_message_t.Insert i)
-          betree_node_lookup_first_message_for_key_back key msgs msgs2
-      | betree_message_t.Delete =>
-        do
-          let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0
-          let msgs2 ←
-            betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs1
-              (key, betree_message_t.Delete)
-          betree_node_lookup_first_message_for_key_back key msgs msgs2
-      | betree_message_t.Upsert s =>
-        do
-          let p ← betree_list_hd_fwd (UInt64 × betree_message_t) msgs0
-          let (_, m) := p
-          match h: m with
-          | betree_message_t.Insert prev =>
-            do
-              let v ← betree_upsert_update_fwd (Option.some prev) s
-              let msgs1 ←
-                betree_list_pop_front_back (UInt64 × betree_message_t) msgs0
-              let msgs2 ←
-                betree_list_push_front_fwd_back (UInt64 × betree_message_t)
-                  msgs1 (key, betree_message_t.Insert v)
-              betree_node_lookup_first_message_for_key_back key msgs msgs2
-          | betree_message_t.Delete =>
-            do
-              let v ← betree_upsert_update_fwd Option.none s
-              let msgs1 ←
-                betree_list_pop_front_back (UInt64 × betree_message_t) msgs0
-              let msgs2 ←
-                betree_list_push_front_fwd_back (UInt64 × betree_message_t)
-                  msgs1 (key, betree_message_t.Insert v)
-              betree_node_lookup_first_message_for_key_back key msgs msgs2
-          | betree_message_t.Upsert ufs =>
-            do
-              let msgs1 ←
-                betree_node_lookup_first_message_after_key_fwd key msgs0
-              let msgs2 ←
-                betree_list_push_front_fwd_back (UInt64 × betree_message_t)
-                  msgs1 (key, betree_message_t.Upsert s)
-              let msgs3 ←
-                betree_node_lookup_first_message_after_key_back key msgs0 msgs2
-              betree_node_lookup_first_message_for_key_back key msgs msgs3
-    else
-      do
-        let msgs1 ←
-          betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs0
-            (key, new_msg)
-        betree_node_lookup_first_message_for_key_back key msgs msgs1
-
-/- [betree_main::betree::Node::{5}::apply_messages_to_internal] -/
-def betree_node_apply_messages_to_internal_fwd_back
-  (msgs : betree_list_t (UInt64 × betree_message_t))
-  (new_msgs : betree_list_t (UInt64 × betree_message_t)) :
-  (Result (betree_list_t (UInt64 × betree_message_t)))
-  :=
-  match h: new_msgs with
-  | betree_list_t.Cons new_msg new_msgs_tl =>
-    do
-      let (i, m) := new_msg
-      let msgs0 ← betree_node_apply_to_internal_fwd_back msgs i m
-      betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl
-  | betree_list_t.Nil => Result.ret msgs
-termination_by betree_node_apply_messages_to_internal_fwd_back msgs new_msgs =>
-  betree_node_apply_messages_to_internal_terminates msgs new_msgs
-decreasing_by betree_node_apply_messages_to_internal_decreases msgs new_msgs
-
-/- [betree_main::betree::Node::{5}::apply_messages] -/
-mutual def betree_node_apply_messages_fwd
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) :
-  (Result (State × Unit))
-  :=
-  match h: self with
-  | betree_node_t.Internal node =>
-    do
-      let (mkbetree_internal_t i i0 n n0) := node
-      let (st0, content) ← betree_load_internal_node_fwd i st
-      let content0 ←
-        betree_node_apply_messages_to_internal_fwd_back content msgs
-      let num_msgs ←
-        betree_list_len_fwd (UInt64 × betree_message_t) content0
-      if h: num_msgs >= params.betree_params_min_flush_size
-      then
-        do
-          let (st1, content1) ←
-            betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params
-              node_id_cnt content0 st0
-          let (node0, _) ←
-            betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params
-              node_id_cnt content0 st0
-          let (mkbetree_internal_t i1 _ _ _) := node0
-          let (st2, _) ← betree_store_internal_node_fwd i1 content1 st1
-          Result.ret (st2, ())
-      else
-        do
-          let (st1, _) ← betree_store_internal_node_fwd i content0 st0
-          Result.ret (st1, ())
-  | betree_node_t.Leaf node =>
-    do
-      let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs
-      let len ← betree_list_len_fwd (UInt64 × UInt64) content0
-      let i ← UInt64.checked_mul (UInt64.ofNatCore 2 (by intlit))
-        params.betree_params_split_size
-      if h: len >= i
-      then
-        do
-          let (st1, _) ←
-            betree_leaf_split_fwd node content0 params node_id_cnt st0
-          let (st2, _) ←
-            betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
-              st1
-          Result.ret (st2, ())
-      else
-        do
-          let (st1, _) ←
-            betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
-          Result.ret (st1, ())
-termination_by betree_node_apply_messages_fwd self params node_id_cnt msgs st
-  =>
-  betree_node_apply_messages_terminates self params node_id_cnt msgs st
-decreasing_by
-  betree_node_apply_messages_decreases self params node_id_cnt msgs st
-
-/- [betree_main::betree::Node::{5}::apply_messages] -/
-def betree_node_apply_messages_back
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) :
-  (Result (betree_node_t × betree_node_id_counter_t))
-  :=
-  match h: self with
-  | betree_node_t.Internal node =>
-    do
-      let (mkbetree_internal_t i i0 n n0) := node
-      let (st0, content) ← betree_load_internal_node_fwd i st
-      let content0 ←
-        betree_node_apply_messages_to_internal_fwd_back content msgs
-      let num_msgs ←
-        betree_list_len_fwd (UInt64 × betree_message_t) content0
-      if h: num_msgs >= params.betree_params_min_flush_size
-      then
-        do
-          let (st1, content1) ←
-            betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params
-              node_id_cnt content0 st0
-          let (node0, node_id_cnt0) ←
-            betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params
-              node_id_cnt content0 st0
-          let (mkbetree_internal_t i1 i2 n1 n2) := node0
-          let _ ← betree_store_internal_node_fwd i1 content1 st1
-          Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1 n2),
-            node_id_cnt0)
-      else
-        do
-          let _ ← betree_store_internal_node_fwd i content0 st0
-          Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n n0),
-            node_id_cnt)
-  | betree_node_t.Leaf node =>
-    do
-      let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st
-      let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs
-      let len ← betree_list_len_fwd (UInt64 × UInt64) content0
-      let i ← UInt64.checked_mul (UInt64.ofNatCore 2 (by intlit))
-        params.betree_params_split_size
-      if h: len >= i
-      then
-        do
-          let (st1, new_node) ←
-            betree_leaf_split_fwd node content0 params node_id_cnt st0
-          let _ ←
-            betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
-              st1
-          let node_id_cnt0 ←
-            betree_leaf_split_back node content0 params node_id_cnt st0
-          Result.ret (betree_node_t.Internal new_node, node_id_cnt0)
-      else
-        do
-          let _ ← betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
-          Result.ret (betree_node_t.Leaf { node with betree_leaf_size := len },
-            node_id_cnt)
-termination_by betree_node_apply_messages_back self params node_id_cnt msgs st
-  =>
-  betree_node_apply_messages_terminates self params node_id_cnt msgs st
-decreasing_by
-  betree_node_apply_messages_decreases self params node_id_cnt msgs st
-
-/- [betree_main::betree::Internal::{4}::flush] -/
-def betree_internal_flush_fwd
-  (self : betree_internal_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (UInt64 × betree_message_t)) (st : State) :
-  (Result (State × (betree_list_t (UInt64 × betree_message_t))))
-  :=
-  do
-    let (mkbetree_internal_t _ i n n0) := self
-    let p ← betree_list_partition_at_pivot_fwd betree_message_t content i
-    let (msgs_left, msgs_right) := p
-    let len_left ← betree_list_len_fwd (UInt64 × betree_message_t) msgs_left
-    if h: len_left >= params.betree_params_min_flush_size
-    then
-      do
-        let (st0, _) ←
-          betree_node_apply_messages_fwd n params node_id_cnt msgs_left st
-        let (_, node_id_cnt0) ←
-          betree_node_apply_messages_back n params node_id_cnt msgs_left st
-        let len_right ←
-          betree_list_len_fwd (UInt64 × betree_message_t) msgs_right
-        if h: len_right >= params.betree_params_min_flush_size
-        then
-          do
-            let (st1, _) ←
-              betree_node_apply_messages_fwd n0 params node_id_cnt0 msgs_right
-                st0
-            let _ ←
-              betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right
-                st0
-            Result.ret (st1, betree_list_t.Nil)
-        else Result.ret (st0, msgs_right)
-    else
-      do
-        let (st0, _) ←
-          betree_node_apply_messages_fwd n0 params node_id_cnt msgs_right st
-        let _ ←
-          betree_node_apply_messages_back n0 params node_id_cnt msgs_right st
-        Result.ret (st0, msgs_left)
-termination_by betree_internal_flush_fwd self params node_id_cnt content st =>
-  betree_internal_flush_terminates self params node_id_cnt content st
-decreasing_by
-  betree_internal_flush_decreases self params node_id_cnt content st
-
-/- [betree_main::betree::Internal::{4}::flush] -/
-def betree_internal_flush_back
-  (self : betree_internal_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (UInt64 × betree_message_t)) (st : State) :
-  (Result (betree_internal_t × betree_node_id_counter_t))
-  :=
-  do
-    let (mkbetree_internal_t i i0 n n0) := self
-    let p ← betree_list_partition_at_pivot_fwd betree_message_t content i0
-    let (msgs_left, msgs_right) := p
-    let len_left ← betree_list_len_fwd (UInt64 × betree_message_t) msgs_left
-    if h: len_left >= params.betree_params_min_flush_size
-    then
-      do
-        let (st0, _) ←
-          betree_node_apply_messages_fwd n params node_id_cnt msgs_left st
-        let (n1, node_id_cnt0) ←
-          betree_node_apply_messages_back n params node_id_cnt msgs_left st
-        let len_right ←
-          betree_list_len_fwd (UInt64 × betree_message_t) msgs_right
-        if h: len_right >= params.betree_params_min_flush_size
-        then
-          do
-            let (n2, node_id_cnt1) ←
-              betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right
-                st0
-            Result.ret (mkbetree_internal_t i i0 n1 n2, node_id_cnt1)
-        else Result.ret (mkbetree_internal_t i i0 n1 n0, node_id_cnt0)
-    else
-      do
-        let (n1, node_id_cnt0) ←
-          betree_node_apply_messages_back n0 params node_id_cnt msgs_right st
-        Result.ret (mkbetree_internal_t i i0 n n1, node_id_cnt0)
-termination_by betree_internal_flush_back self params node_id_cnt content st =>
-  betree_internal_flush_terminates self params node_id_cnt content st
-decreasing_by
-  betree_internal_flush_decreases self params node_id_cnt content st
-
-/- [betree_main::betree::Node::{5}::apply] -/
-def betree_node_apply_fwd
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t) (key : UInt64)
-  (new_msg : betree_message_t) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let l := betree_list_t.Nil
-    let (st0, _) ←
-      betree_node_apply_messages_fwd self params node_id_cnt
-        (betree_list_t.Cons (key, new_msg) l) st
-    let _ ←
-      betree_node_apply_messages_back self params node_id_cnt
-        (betree_list_t.Cons (key, new_msg) l) st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::Node::{5}::apply] -/
-def betree_node_apply_back
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t) (key : UInt64)
-  (new_msg : betree_message_t) (st : State) :
-  Result (betree_node_t × betree_node_id_counter_t)
-  :=
-  let l := betree_list_t.Nil
-  betree_node_apply_messages_back self params node_id_cnt (betree_list_t.Cons
-    (key, new_msg) l) st
-
-/- [betree_main::betree::BeTree::{6}::new] -/
-def betree_be_tree_new_fwd
-  (min_flush_size : UInt64) (split_size : UInt64) (st : State) :
-  Result (State × betree_be_tree_t)
-  :=
-  do
-    let node_id_cnt ← betree_node_id_counter_new_fwd
-    let id ← betree_node_id_counter_fresh_id_fwd node_id_cnt
-    let (st0, _) ← betree_store_leaf_node_fwd id betree_list_t.Nil st
-    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
-    Result.ret (st0,
-      {
-        betree_be_tree_params :=
-          {
-            betree_params_min_flush_size := min_flush_size,
-            betree_params_split_size := split_size
-          },
-        betree_be_tree_node_id_cnt := node_id_cnt0,
-        betree_be_tree_root :=
-          (betree_node_t.Leaf
-            {
-              betree_leaf_id := id,
-              betree_leaf_size := (UInt64.ofNatCore 0 (by intlit))
-            })
-      })
-
-/- [betree_main::betree::BeTree::{6}::apply] -/
-def betree_be_tree_apply_fwd
-  (self : betree_be_tree_t) (key : UInt64) (msg : betree_message_t)
-  (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
-        self.betree_be_tree_node_id_cnt key msg st
-    let _ ←
-      betree_node_apply_back self.betree_be_tree_root
-        self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::BeTree::{6}::apply] -/
-def betree_be_tree_apply_back
-  (self : betree_be_tree_t) (key : UInt64) (msg : betree_message_t)
-  (st : State) :
-  Result betree_be_tree_t
-  :=
-  do
-    let (n, nic) ←
-      betree_node_apply_back self.betree_be_tree_root
-        self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st
-    Result.ret
-      { self with betree_be_tree_node_id_cnt := nic, betree_be_tree_root := n }
-
-/- [betree_main::betree::BeTree::{6}::insert] -/
-def betree_be_tree_insert_fwd
-  (self : betree_be_tree_t) (key : UInt64) (value : UInt64) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree_be_tree_apply_fwd self key (betree_message_t.Insert value) st
-    let _ ←
-      betree_be_tree_apply_back self key (betree_message_t.Insert value) st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::BeTree::{6}::insert] -/
-def betree_be_tree_insert_back
-  (self : betree_be_tree_t) (key : UInt64) (value : UInt64) (st : State) :
-  Result betree_be_tree_t
-  :=
-  betree_be_tree_apply_back self key (betree_message_t.Insert value) st
-
-/- [betree_main::betree::BeTree::{6}::delete] -/
-def betree_be_tree_delete_fwd
-  (self : betree_be_tree_t) (key : UInt64) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree_be_tree_apply_fwd self key betree_message_t.Delete st
-    let _ ← betree_be_tree_apply_back self key betree_message_t.Delete st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::BeTree::{6}::delete] -/
-def betree_be_tree_delete_back
-  (self : betree_be_tree_t) (key : UInt64) (st : State) :
-  Result betree_be_tree_t
-  :=
-  betree_be_tree_apply_back self key betree_message_t.Delete st
-
-/- [betree_main::betree::BeTree::{6}::upsert] -/
-def betree_be_tree_upsert_fwd
-  (self : betree_be_tree_t) (key : UInt64) (upd : betree_upsert_fun_state_t)
-  (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree_be_tree_apply_fwd self key (betree_message_t.Upsert upd) st
-    let _ ←
-      betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::BeTree::{6}::upsert] -/
-def betree_be_tree_upsert_back
-  (self : betree_be_tree_t) (key : UInt64) (upd : betree_upsert_fun_state_t)
-  (st : State) :
-  Result betree_be_tree_t
-  :=
-  betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st
-
-/- [betree_main::betree::BeTree::{6}::lookup] -/
-def betree_be_tree_lookup_fwd
-  (self : betree_be_tree_t) (key : UInt64) (st : State) :
-  Result (State × (Option UInt64))
-  :=
-  betree_node_lookup_fwd self.betree_be_tree_root key st
-
-/- [betree_main::betree::BeTree::{6}::lookup] -/
-def betree_be_tree_lookup_back
-  (self : betree_be_tree_t) (key : UInt64) (st : State) :
-  Result betree_be_tree_t
-  :=
-  do
-    let n ← betree_node_lookup_back self.betree_be_tree_root key st
-    Result.ret { self with betree_be_tree_root := n }
-
-/- [betree_main::main] -/
-def main_fwd : Result Unit :=
-  Result.ret ()
-
-/- Unit test for [betree_main::main] -/
-#assert (main_fwd == .ret ())
-
diff --git a/tests/lean/betree/BetreeMain/Opaque.lean b/tests/lean/betree/BetreeMain/Opaque.lean
deleted file mode 100644
index b3db37c2..00000000
--- a/tests/lean/betree/BetreeMain/Opaque.lean
+++ /dev/null
@@ -1,33 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [betree_main]: opaque function definitions
-import Base.Primitives
-import BetreeMain.Types
-
-structure OpaqueDefs where
-  
-  /- [betree_main::betree_utils::load_internal_node] -/
-  betree_utils_load_internal_node_fwd
-    :
-    UInt64 -> State -> Result (State × (betree_list_t (UInt64 ×
-      betree_message_t)))
-  
-  /- [betree_main::betree_utils::store_internal_node] -/
-  betree_utils_store_internal_node_fwd
-    :
-    UInt64 -> betree_list_t (UInt64 × betree_message_t) -> State -> Result
-      (State × Unit)
-  
-  /- [betree_main::betree_utils::load_leaf_node] -/
-  betree_utils_load_leaf_node_fwd
-    : UInt64 -> State -> Result (State × (betree_list_t (UInt64 × UInt64)))
-  
-  /- [betree_main::betree_utils::store_leaf_node] -/
-  betree_utils_store_leaf_node_fwd
-    :
-    UInt64 -> betree_list_t (UInt64 × UInt64) -> State -> Result (State ×
-      Unit)
-  
-  /- [core::option::Option::{0}::unwrap] -/
-  core_option_option_unwrap_fwd
-    (T : Type) : Option T -> State -> Result (State × T)
-  
diff --git a/tests/lean/betree/BetreeMain/Types.lean b/tests/lean/betree/BetreeMain/Types.lean
deleted file mode 100644
index 32634e30..00000000
--- a/tests/lean/betree/BetreeMain/Types.lean
+++ /dev/null
@@ -1,55 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [betree_main]: type definitions
-import Base.Primitives
-
-/- [betree_main::betree::List] -/
-inductive betree_list_t (T : Type) :=
-| Cons : T -> betree_list_t T -> betree_list_t T
-| Nil : betree_list_t T
-
-/- [betree_main::betree::UpsertFunState] -/
-inductive betree_upsert_fun_state_t :=
-| Add : UInt64 -> betree_upsert_fun_state_t
-| Sub : UInt64 -> betree_upsert_fun_state_t
-
-/- [betree_main::betree::Message] -/
-inductive betree_message_t :=
-| Insert : UInt64 -> betree_message_t
-| Delete : betree_message_t
-| Upsert : betree_upsert_fun_state_t -> betree_message_t
-
-/- [betree_main::betree::Leaf] -/
-structure betree_leaf_t where
-  betree_leaf_id : UInt64
-  betree_leaf_size : UInt64
-
-/- [betree_main::betree::Node] -/
-mutual inductive betree_node_t :=
-| Internal : betree_internal_t -> betree_node_t
-| Leaf : betree_leaf_t -> betree_node_t
-
-/- [betree_main::betree::Internal] -/
-inductive betree_internal_t :=
-  betree_internal_id : UInt64
-  betree_internal_pivot : UInt64
-  betree_internal_left : betree_node_t
-  betree_internal_right : betree_node_t
-
-/- [betree_main::betree::Params] -/
-structure betree_params_t where
-  betree_params_min_flush_size : UInt64
-  betree_params_split_size : UInt64
-
-/- [betree_main::betree::NodeIdCounter] -/
-structure betree_node_id_counter_t where
-  betree_node_id_counter_next_node_id : UInt64
-
-/- [betree_main::betree::BeTree] -/
-structure betree_be_tree_t where
-  betree_be_tree_params : betree_params_t
-  betree_be_tree_node_id_cnt : betree_node_id_counter_t
-  betree_be_tree_root : betree_node_t
-
-/- The state type used in the state-error monad -/
-axiom State : Type
-
diff --git a/tests/lean/betree/lake-manifest.json b/tests/lean/betree/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/betree/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/betree/lakefile.lean b/tests/lean/betree/lakefile.lean
deleted file mode 100644
index ac2cc2d8..00000000
--- a/tests/lean/betree/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «betree_main» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «BetreeMain» {}
diff --git a/tests/lean/betree/lean-toolchain b/tests/lean/betree/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/betree/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21