Exact named statement
∀ x. ∀ y. ∀ z. ∀ n. ∀ m. ∀ k. ¬z = 0 ∧ (¬k = 0 ∧ x · k + m · z = y · k + n · z) → ¬k = 0 ∧ (¬z = 0 ∧ n · z + y · k = m · z + x · k)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: f7d7e191f77999e19d76738748486cbece8288613c749b20716d0a473d6afaba
Bundle SHA-256: 2771ec79c87230edd6493a9bdae4fee95b4f6499905c51932b810e5f95b06a98
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.