val successful_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation
      (sem: semantics_t)
      (transition: transition_t (make_atomic_semantics sem))
      (s 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)
val successful_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation
      (sem: semantics_t)
      (transition: transition_t (make_atomic_semantics sem))
      (s 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)
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'
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'
/
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 ->
    transition: Strategies.Semantics.transition_t (Strategies.Atomic.make_atomic_semantics sem) ->
    s: Mksemantics_t?.state_t sem ->
    s': Mksemantics_t?.state_t sem
  -> FStar.Pervasives.Lemma
      (requires
        Strategies.Semantics.next_transition_generic (Strategies.Atomic.make_atomic_semantics sem)
          transition
          s
          s')
      (ensures
        Strategies.Semantics.steps_computation_generic (Strategies.Atomic.make_atomic_semantics sem)
          (Mktransition_t?.actor transition)
          true
          true
          (Mktransition_t?.steps transition)
          s ==
        Strategies.AtomicToRegular.list_of_list_of_steps_computation sem
          (Mktransition_t?.actor transition)
          true
          true
          (Mktransition_t?.steps transition)
          s)
      (decreases Mktransition_t?.steps transition)
Strategies.Semantics.semantics_t Strategies.Semantics.transition_t Strategies.Atomic.make_atomic_semantics Strategies.Semantics.__proj__Mksemantics_t__item__state_t Strategies.AtomicToRegular.successful_generic_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation Strategies.Semantics.__proj__Mktransition_t__item__actor Strategies.Semantics.__proj__Mktransition_t__item__steps Prims.unit Strategies.Semantics.next_transition_generic Prims.squash Prims.eq2 FStar.Pervasives.Native.option Strategies.Semantics.steps_computation_generic Strategies.AtomicToRegular.list_of_list_of_steps_computation Prims.Nil FStar.Pervasives.pattern
let successful_atomic_step_computation_equivalent_to_list_of_list_of_steps_computation
      (sem: semantics_t)
      (transition: transition_t (make_atomic_semantics sem))
      (s 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'