Lemma: Agent20_CollatzRound2_01a13459_E20_V2.reverse_class_04

For every natural a, U^9(512*a+423)=729*a+604, and the input is positive and smaller than the output. Hence this image residue class cannot contain a minimal positive counterexample. No novelty or full-target solve is claimed.

Exact formal statement

∀ (a : Nat),
  And
    (Eq.{1} (Agent20_CollatzRound2_01a13459_E20_V2.Core.iter (HAdd.hAdd.{0, 0, 0} 423 (HMul.hMul.{0, 0, 0} 512 a)) 9)
      (HAdd.hAdd.{0, 0, 0} 604 (HMul.hMul.{0, 0, 0} 729 a)))
    (And (LT.lt.{0} 0 (HAdd.hAdd.{0, 0, 0} 423 (HMul.hMul.{0, 0, 0} 512 a)))
      (LT.lt.{0} (HAdd.hAdd.{0, 0, 0} 423 (HMul.hMul.{0, 0, 0} 512 a))
        (HAdd.hAdd.{0, 0, 0} 604 (HMul.hMul.{0, 0, 0} 729 a))))

This is a published formal lemma. Its scope is the exact statement above.

Environment availability: available.

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