import Mathlib

def lcs_spec (s t : List Char) : Nat :=
  match s, t with
  | [], _ => 0
  | _, [] => 0
  | x :: xs, y :: ys =>
    if x = y then 1 + lcs_spec xs ys
    else max (lcs_spec xs (y :: ys)) (lcs_spec (x :: xs) ys)

-- Precondition definitions
@[reducible, simp]
def solve_longest_common_subsequence_precond (s t : List Char) : Prop :=
  -- !benchmark @start precond
  s.length ≤ 3000 ∧ t.length ≤ 3000
  -- !benchmark @end precond

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

-- Main function definition
def solve_longest_common_subsequence (s t : List Char)
    (h_precond : solve_longest_common_subsequence_precond s t) : Nat :=
  -- !benchmark @start code
  sorry
  -- !benchmark @end code

-- Postcondition definitions
@[reducible, simp]
def solve_longest_common_subsequence_postcond (s t : List Char) (result : Nat)
    (_ : solve_longest_common_subsequence_precond s t) : Prop :=
  -- !benchmark @start postcond
  result = lcs_spec s t
  -- !benchmark @end postcond

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

-- Proof content
theorem solve_longest_common_subsequence_postcond_satisfied (s t : List Char)
    (h_precond : solve_longest_common_subsequence_precond s t) :
    solve_longest_common_subsequence_postcond s t (solve_longest_common_subsequence s t h_precond) h_precond := by
  -- !benchmark @start proof
  sorry
  -- !benchmark @end proof