Exact named statement
∀ x. ∀ y. ∀ z. ∀ n. ¬z = 0 → ¬n = 0 → ¬z = 0 ∧ (¬z · n = 0 ∧ x · (z · n) + y · n · z = y · (z · n) + x · n · 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: b07b8ed827c19e15e27f3dd746a89445ec5326208631ec81e298da144cd716fb
Bundle SHA-256: 429fa6e2ea7a800c115327a3c465951c47da8e46ffcc71e40e3654e61c1303f0
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.