Exact named statement
∀ x. ∀ y. ∀ z. ∀ n. ∀ m. ∀ k. ∀ i. ∀ j. ∀ u. ¬z = 0 ∧ (¬k = 0 ∧ x · k + m · z = y · k + n · z) → ¬k = 0 ∧ (¬u = 0 ∧ n · u + j · k = m · u + i · k) → ¬z = 0 ∧ (¬u = 0 ∧ x · u + j · z = y · u + i · z)No displayed named abbreviation.
Complete certificate and independent checks
1 actual local proof nodes. Each node carries its complete ordinary HA proof body.
Full canonical proof bundle · Original HA receipt · Independent Lean receipt
Target SHA-256: ece8e6152f2026a946640ae397e7bb249f4e0afa100380d3831522708328c8e8
Bundle SHA-256: 44f7e7884fd34f582768032ea2b91b9a24e45744b83f23368eae49755d0aebbf
Checked statement containment
These exact targets occur inside this certificate. These links summarize containment, not direct dependency arrows; the downloadable bundle records every private lemma and ordered edge.
Scope
full named rational foundation not IR001
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.