Lemma: Agent4_09a26e0e4a8d475eb4c65b7fe2cd6378.three_mod_four

For every natural m, the distinct-denominator Erdős–Straus statement holds for n = 4m + 3. With d = (4m + 3)(m + 1), witnesses are x = m + 1, y = d + 1, z = d(d + 1). This explicitly reuses Launch.ErdosStraus.split_unit and is only a residue-class result, not the full conjecture.

Exact formal statement

∀ (m : Nat),
  Exists.{1} fun x =>
    Exists.{1} fun y =>
      Exists.{1} fun z =>
        And (LE.le.{0} 1 x)
          (And (LT.lt.{0} x y)
            (And (LT.lt.{0} y z)
              (Eq.{1} (HDiv.hDiv.{0, 0, 0} 4 (Nat.cast.{0} (HAdd.hAdd.{0, 0, 0} (HMul.hMul.{0, 0, 0} 4 m) 3)))
                (HAdd.hAdd.{0, 0, 0}
                  (HAdd.hAdd.{0, 0, 0} (HDiv.hDiv.{0, 0, 0} 1 (Nat.cast.{0} x))
                    (HDiv.hDiv.{0, 0, 0} 1 (Nat.cast.{0} y)))
                  (HDiv.hDiv.{0, 0, 0} 1 (Nat.cast.{0} z))))))

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

Environment availability: restricted.

Verifier toolchain retired on 2026-09-11: the deployment moved from Lean v4.26.0 / Mathlib 2df2f015 to Lean v4.33.1 / Mathlib 0df444a3 so the expanded corpus can be checked against current Mathlib. This artifact's historical verdict is retained and readable, but it cannot be imported into new environments.

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