import Mathlib

-- Precondition definitions
@[reducible, simp]
def longest_palindromic_substring_precond (s : Array UInt8) : Prop :=
  -- !benchmark @start precond
  s.size ≤ 1000000
  -- !benchmark @end precond

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

-- Main function definitions
def longest_palindromic_substring (s : Array UInt8)
    (_ : longest_palindromic_substring_precond s) :
    Nat × Nat :=
  -- !benchmark @start code
  sorry
  -- !benchmark @end code

-- Helper definitions
def is_valid_subrange (s : Array UInt8) (start len : Nat) : Prop :=
  start + len ≤ s.size

-- A sequence slice s[start, start+len) is a palindrome if for all i < len,
-- s[start + i] == s[start + len - 1 - i]
def is_palindrome_slice (s : Array UInt8) (start len : Nat) : Prop :=
  ∀ i, i < len → s.getD (start + i) 0 = s.getD (start + len - 1 - i) 0

-- Postcondition definitions
@[reducible, simp]
def longest_palindromic_substring_postcond
    (s : Array UInt8) (result : Nat × Nat)
    (_ : longest_palindromic_substring_precond s) : Prop :=
  -- !benchmark @start postcond
  let (start, len) := result
  is_valid_subrange s start len ∧
  is_palindrome_slice s start len ∧
  (∀ i l, is_valid_subrange s i l → is_palindrome_slice s i l → l ≤ len)
  -- !benchmark @end postcond

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

-- Proof content
theorem longest_palindromic_substring_postcond_satisfied
    (s : Array UInt8) (h_precond : longest_palindromic_substring_precond s) :
    longest_palindromic_substring_postcond
      s (longest_palindromic_substring s h_precond) h_precond := by
  -- !benchmark @start proof
  sorry
  -- !benchmark @end proof