val flatten_steps_preserves_eval_result
      (sem: semantics_t)
      (actor: sem.actor_t)
      (starts_atomic_block ends_atomic_block: bool)
      (flattened_steps: list sem.step_t)
      (unflattened_steps: list (list sem.step_t))
      (s: sem.state_t)
    : Lemma
      (requires
        flattened_steps == flatten unflattened_steps /\
        (forall steps. contains_ubool steps unflattened_steps ==> Cons? steps) /\
        Some? (list_of_list_of_steps_computation sem
              actor
              starts_atomic_block
              ends_atomic_block
              unflattened_steps
              s))
      (ensures
        (steps_computation_generic sem actor starts_atomic_block ends_atomic_block flattened_steps s
        ) ==
        (list_of_list_of_steps_computation sem
            actor
            starts_atomic_block
            ends_atomic_block
            unflattened_steps
            s))
      (decreases unflattened_steps)
val flatten_steps_preserves_eval_result
      (sem: semantics_t)
      (actor: sem.actor_t)
      (starts_atomic_block ends_atomic_block: bool)
      (flattened_steps: list sem.step_t)
      (unflattened_steps: list (list sem.step_t))
      (s: sem.state_t)
    : Lemma
      (requires
        flattened_steps == flatten unflattened_steps /\
        (forall steps. contains_ubool steps unflattened_steps ==> Cons? steps) /\
        Some? (list_of_list_of_steps_computation sem
              actor
              starts_atomic_block
              ends_atomic_block
              unflattened_steps
              s))
      (ensures
        (steps_computation_generic sem actor starts_atomic_block ends_atomic_block flattened_steps s
        ) ==
        (list_of_list_of_steps_computation sem
            actor
            starts_atomic_block
            ends_atomic_block
            unflattened_steps
            s))
      (decreases unflattened_steps)
let rec flatten_steps_preserves_eval_result
  (sem: semantics_t)
  (actor: sem.actor_t)
  (starts_atomic_block: bool)
  (ends_atomic_block: bool)
  (flattened_steps: list sem.step_t)
  (unflattened_steps: list (list sem.step_t))
  (s: sem.state_t)
  : Lemma
  (requires   flattened_steps == flatten unflattened_steps
            /\ (forall steps. contains_ubool steps unflattened_steps ==> Cons? steps)
            /\ Some? (list_of_list_of_steps_computation sem actor starts_atomic_block ends_atomic_block
                       unflattened_steps s))
  (ensures  (steps_computation_generic sem actor starts_atomic_block ends_atomic_block flattened_steps s) ==
            (list_of_list_of_steps_computation sem actor starts_atomic_block ends_atomic_block unflattened_steps s))
  (decreases unflattened_steps) =
  match unflattened_steps with
  | [] -> ()
  | [last_atomic_step] -> append_nil_is_identity last_atomic_step
  | first_atomic_step :: remaining_unflattened_steps ->
     let remaining_steps = flatten remaining_unflattened_steps in
     assert (contains_ubool first_atomic_step unflattened_steps);
     steps_then_steps_computation_equivalent_to_append_compute sem actor starts_atomic_block ends_atomic_block
       first_atomic_step remaining_steps s;
     (match steps_computation_generic sem actor starts_atomic_block false first_atomic_step s with
      | None -> ()
      | Some s' -> flatten_steps_preserves_eval_result sem actor false ends_atomic_block remaining_steps
                    remaining_unflattened_steps s')
module Strategies.AtomicToRegular

open Armada.Action
open Armada.Program
open Armada.State
open Armada.Statement
open Armada.Step
open Armada.Transition
open Spec.Behavior
open FStar.List.Tot
open Spec.List
open Spec.Ubool
open Strategies.Atomic
open Util.Behavior
open Util.List
open Util.Nth

let steps_then_steps_computation
  (sem: semantics_t)
  (actor: sem.actor_t)
  (starts_atomic_block: bool)
  (ends_atomic_block: bool)
  (steps1: list sem.step_t)
  (steps2: list sem.step_t)
  (s: sem.state_t)
  : GTot (option sem.state_t) =
  match steps_computation_generic sem actor starts_atomic_block false steps1 s with
  | None -> None
  | Some s' -> steps_computation_generic sem actor false ends_atomic_block steps2 s'

let rec steps_then_steps_computation_equivalent_to_append_compute
  (sem: semantics_t)
  (actor: sem.actor_t)
  (starts_atomic_block: bool)
  (ends_atomic_block: bool)
  (steps1: list sem.step_t)
  (steps2: list sem.step_t)
  (s: sem.state_t)
  : Lemma
  (requires Cons? steps1 /\ Cons? steps2)
  (ensures  steps_then_steps_computation sem actor starts_atomic_block ends_atomic_block steps1 steps2 s ==
            steps_computation_generic sem actor starts_atomic_block ends_atomic_block (append steps1 steps2) s)
  (decreases steps1) =
  match steps1 with
  | [last_step] -> ()
  | first_step :: remaining_steps ->
      (match step_computation_generic sem actor starts_atomic_block false first_step s with
       | None -> ()
       | Some s' -> steps_then_steps_computation_equivalent_to_append_compute sem actor
                     false ends_atomic_block remaining_steps steps2 s')

let rec list_of_list_of_steps_computation
  (sem: semantics_t)
  (actor: sem.actor_t)
  (starts_atomic_block: bool)
  (ends_atomic_block: bool)
  (steps: list (list sem.step_t))
  (s: sem.state_t)
  : GTot (option sem.state_t)
      (decreases steps) =
  match steps with
  | [] -> None
  | [last_step] -> steps_computation_generic sem actor starts_atomic_block ends_atomic_block last_step s
  | first_step :: remaining_steps ->
      (match steps_computation_generic sem actor starts_atomic_block false first_step s with
       | None -> None
       | Some s' -> list_of_list_of_steps_computation sem actor false ends_atomic_block remaining_steps s')

let rec successful_generic_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation
  (sem: semantics_t)
  (actor: sem.actor_t)
  (starts_atomic_block: bool)
  (ends_atomic_block: bool)
  (steps: list (list sem.step_t))
  (s: sem.state_t)
  (s': sem.state_t)
  : Lemma (requires Some? (steps_computation_generic (make_atomic_semantics sem) actor starts_atomic_block
                             ends_atomic_block steps s))
          (ensures  steps_computation_generic (make_atomic_semantics sem) actor starts_atomic_block
                      ends_atomic_block steps s ==
                        list_of_list_of_steps_computation sem actor starts_atomic_block ends_atomic_block steps s)
          (decreases steps) =
  match steps with
  | [] -> ()
  | [last_atomic_step] -> ()
  | first_step :: remaining_steps ->
      let s_mid = Some?.v (steps_computation_generic sem actor starts_atomic_block false first_step s) in
      successful_generic_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation sem actor false
        ends_atomic_block remaining_steps s_mid s'

let successful_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation
  (sem: semantics_t)
  (transition: transition_t (make_atomic_semantics sem))
  (s: sem.state_t)
  (s': sem.state_t)
  : Lemma (requires next_transition_generic (make_atomic_semantics sem) transition s s')
          (ensures  steps_computation_generic (make_atomic_semantics sem) transition.actor true true
                      transition.steps s ==
                      list_of_list_of_steps_computation sem transition.actor true true transition.steps s)
          (decreases transition.steps) =
  successful_generic_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation sem transition.actor
    true true transition.steps s s'
/
Util.Nth.fst.checked Util.List.fst.checked Util.Behavior.fst.checked Strategies.Atomic.fst.checked Spec.Ubool.fst.checked Spec.List.fst.checked Spec.Behavior.fst.checked prims.fst.checked FStar.Tactics.V2.fst.checked FStar.Tactics.Effect.fsti.checked FStar.Pervasives.fsti.checked FStar.List.Tot.fst.checked FStar.Classical.Sugar.fsti.checked Armada.Transition.fst.checked Armada.Step.fst.checked Armada.Statement.fst.checked Armada.State.fst.checked Armada.Program.fst.checked Armada.Action.fst.checked
Strategies.AtomicToRegular.fst

    sem: Strategies.Semantics.semantics_t ->
    actor: Mksemantics_t?.actor_t sem ->
    starts_atomic_block: Prims.bool ->
    ends_atomic_block: Prims.bool ->
    flattened_steps: Prims.list (Mksemantics_t?.step_t sem) ->
    unflattened_steps: Prims.list (Prims.list (Mksemantics_t?.step_t sem)) ->
    s: Mksemantics_t?.state_t sem
  -> FStar.Pervasives.Lemma
      (requires
        flattened_steps == FStar.List.Tot.Base.flatten unflattened_steps /\
        (forall (steps: Prims.list (Mksemantics_t?.step_t sem)).
            Spec.List.contains_ubool steps unflattened_steps ==> Cons? steps) /\
        Some? (Strategies.AtomicToRegular.list_of_list_of_steps_computation sem
              actor
              starts_atomic_block
              ends_atomic_block
              unflattened_steps
              s))
      (ensures
        Strategies.Semantics.steps_computation_generic sem
          actor
          starts_atomic_block
          ends_atomic_block
          flattened_steps
          s ==
        Strategies.AtomicToRegular.list_of_list_of_steps_computation sem
          actor
          starts_atomic_block
          ends_atomic_block
          unflattened_steps
          s)
      (decreases unflattened_steps)
Strategies.Semantics.semantics_t Strategies.Semantics.__proj__Mksemantics_t__item__actor_t Prims.bool Prims.list Strategies.Semantics.__proj__Mksemantics_t__item__step_t Strategies.Semantics.__proj__Mksemantics_t__item__state_t Util.List.append_nil_is_identity Strategies.Semantics.steps_computation_generic Strategies.AtomicToRegular.flatten_steps_preserves_eval_result Prims.unit Strategies.AtomicToRegular.steps_then_steps_computation_equivalent_to_append_compute Prims._assert Spec.List.contains_ubool FStar.List.Tot.Base.flatten Prims.l_and Prims.eq2 Prims.l_Forall Prims.l_imp Prims.b2t Prims.uu___is_Cons FStar.Pervasives.Native.uu___is_Some Strategies.AtomicToRegular.list_of_list_of_steps_computation Prims.squash FStar.Pervasives.Native.option Prims.Nil FStar.Pervasives.pattern
let rec flatten_steps_preserves_eval_result
      (sem: semantics_t)
      (actor: sem.actor_t)
      (starts_atomic_block ends_atomic_block: bool)
      (flattened_steps: list sem.step_t)
      (unflattened_steps: list (list sem.step_t))
      (s: sem.state_t)
    : Lemma
      (requires
        flattened_steps == flatten unflattened_steps /\
        (forall steps. contains_ubool steps unflattened_steps ==> Cons? steps) /\
        Some? (list_of_list_of_steps_computation sem
              actor
              starts_atomic_block
              ends_atomic_block
              unflattened_steps
              s))
      (ensures
        (steps_computation_generic sem actor starts_atomic_block ends_atomic_block flattened_steps s
        ) ==
        (list_of_list_of_steps_computation sem
            actor
            starts_atomic_block
            ends_atomic_block
            unflattened_steps
            s))
      (decreases unflattened_steps) =
  
match unflattened_steps with
| [] -> ()
| [last_atomic_step] -> append_nil_is_identity last_atomic_step
| first_atomic_step :: remaining_unflattened_steps ->
  let remaining_steps = flatten remaining_unflattened_steps in
  assert (contains_ubool first_atomic_step unflattened_steps);
  steps_then_steps_computation_equivalent_to_append_compute sem
    actor
    starts_atomic_block
    ends_atomic_block
    first_atomic_step
    remaining_steps
    s;
  (match steps_computation_generic sem actor starts_atomic_block false first_atomic_step s with
    | None -> ()
    | Some s' ->
      flatten_steps_preserves_eval_result sem
        actor
        false
        ends_atomic_block
        remaining_steps
        remaining_unflattened_steps
        s')