Exact named statement
∀ x. ∀ y. ∀ z. ∀ n. ∀ m. ∀ k. ¬z = 0 ∧ (¬k = 0 ∧ x · k + m · z = y · k + n · z) → ¬z = 0 ∧ (¬k = 0 ∧ y · k + n · z = x · k + m · 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: c23712611e4fa9d7630c08e3f0543d4d8d6df6e7b03c01b0b5c02da8ea18c135
Bundle SHA-256: 73a5ab398f643e71657f904a78d43e58a8c327ded87ae1eecb6376a5b3389aba
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.