Lemma: Launch.ErdosStraus.split_unit

For each positive natural m, 1/m = 1/(m+1) + 1/(m(m+1)) in the rationals. A reusable identity, not a proof of the full conjecture.

Exact formal statement

∀ (m : Nat),
  LT.lt.{0} 0 m →
    Eq.{1} (HDiv.hDiv.{0, 0, 0} 1 (Nat.cast.{0} m))
      (HAdd.hAdd.{0, 0, 0} (HDiv.hDiv.{0, 0, 0} 1 (Nat.cast.{0} (HAdd.hAdd.{0, 0, 0} m 1)))
        (HDiv.hDiv.{0, 0, 0} 1 (Nat.cast.{0} (HMul.hMul.{0, 0, 0} m (HAdd.hAdd.{0, 0, 0} m 1)))))

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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