import Mathlib

structure VerifiableQueue (T : Type) where
  data : List T

def VerifiableQueue.view {T} (q : VerifiableQueue T) : List T :=
  q.data

def VerifiableQueue.is_valid {T} (q : VerifiableQueue T) : Prop :=
  True

-- Precondition definitions
@[reducible, simp]
def dequeue_precond {T} (q : VerifiableQueue T) : Prop :=
  -- !benchmark @start precond
  q.is_valid ∧ q.view.length > 0
  -- !benchmark @end precond

-- !benchmark @start auxcode
-- !benchmark @end auxcode

-- Main function definition
-- Returns the projected pair (val, new_queue)
def dequeue {T} (q : VerifiableQueue T)
    (h_precond : dequeue_precond q) : T × VerifiableQueue T :=
  -- !benchmark @start code
  sorry
  -- !benchmark @end code

-- Postcondition definitions
@[reducible, simp]
def dequeue_postcond {T} (q : VerifiableQueue T) (result : T × VerifiableQueue T)
    (_ : dequeue_precond q) : Prop :=
  -- !benchmark @start postcond
  let (val, new_queue) := result
  new_queue.is_valid ∧
  -- Concise & Proof-Free: The old queue consists of the return value followed by the new queue.
  q.view = val :: new_queue.view
  -- !benchmark @end postcond

-- !benchmark @start lemma
-- !benchmark @end lemma

-- Proof content
theorem dequeue_postcond_satisfied {T} (q : VerifiableQueue T)
    (h_precond : dequeue_precond q) :
    dequeue_postcond q (dequeue q h_precond) h_precond := by
  -- !benchmark @start proof
  sorry
  -- !benchmark @end proof