Exact named statement
0 = 0 ∧ (2 · S (2 · (2 · (2 · S (2 · (2 · S (2 · 1)))))) = 2 · S (2 · (2 · (2 · S (2 · (2 · S (2 · 1)))))) ∧ 0 = 0) ∧ (2 · S (2 · S (2 · (2 · (2 · (2 · 1))))) = 2 · S (2 · S (2 · (2 · (2 · (2 · 1))))) ∧ (0 = 0 ∧ 2 · S (2 · (2 · S (2 · (2 · 1)))) = 2 · S (2 · (2 · S (2 · (2 · 1))))))No displayed named abbreviation.
Complete certificate and independent checks
5 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: e8fafbb03e9bf8c595485e474d9a258de8b542defdfbb20a3e3aa745dbc68cbb
Bundle SHA-256: 04e8a51b9815eca002e0b490d9adfc470daa17f2733acf6a30f15489417dcc32
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
complete exact subconjunction child
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.