import Mathlib

-- Precondition definitions
@[reducible, simp]
def exponentiation_precond (b e : UInt64) : Prop :=
  -- !benchmark @start precond
  b.toNat ^ e.toNat ≤ (2 ^ 64 - 1)
  -- !benchmark @end precond

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

-- Main function definitions
def exponentiation (b e : UInt64) (h_precond : exponentiation_precond b e) : UInt64 :=
  -- !benchmark @start code
  sorry
  -- !benchmark @end code

-- Postcondition definitions
@[reducible, simp]
def exponentiation_postcond (b e : UInt64) (result : UInt64) (h_precond : exponentiation_precond b e) : Prop :=
  -- !benchmark @start postcond
  result.toNat = b.toNat ^ e.toNat
  -- !benchmark @end postcond

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

-- Proof content
theorem exponentiation_postcond_satisfied (b e : UInt64)
    (h_precond : exponentiation_precond b e) :
    exponentiation_postcond b e (exponentiation b e h_precond) h_precond := by
  -- !benchmark @start proof
  sorry
  -- !benchmark @end proof