CookLevin.isFormulaStringB_machine_from_transducer_comparator_fixed_child_reduction_child

import Definitions.Def_CookLevin_Verifier

open CookLevin

theorem CookLevin.isFormulaStringB_machine_from_transducer_comparator_fixed_child_reduction_child
    (c1 : Nat) (M1 : Machine) (k1 G1 : Nat) (hwf1 : TuringMachine k1 G1 M1)
    (htrans : ∀ x w : List Bool,
      (execute M1 (startConfig2 k1 (boolsToSymbols x) (boolsToSymbols w)) (c1 * (x.length + 1) ^ 2)).1 = M1.length ∧
      outputOf k1 (execute M1 (startConfig2 k1 (boolsToSymbols x) (boolsToSymbols w)) (c1 * (x.length + 1) ^ 2))
        (c1 * (x.length + 1) ^ 2 + 2) = encodeFormula (decodeFormula x))
    (c2 : Nat) (M2 : Machine) (k2 G2 : Nat) (hwf2 : TuringMachine k2 G2 M2)
    (hcomp : ∀ x y : List Bool,
      DecidesIn M2 k2 (boolsToSymbols x) (boolsToSymbols y)
        (c2 * (x.length + 1))
        (decide (y = x))) :
    ∃ (M : Machine) (k G : Nat),
      TuringMachine k G M ∧
      ∀ x w : List Bool,
        DecidesIn M k (boolsToSymbols x) (boolsToSymbols w)
          (c1 * (x.length + 1) ^ 2 + c2 * (x.length + 1))
          (isFormulaStringB x) := by sorry