ltl-accumulator-verified/verification/Proofs
mrwulf 8795e82865 S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object)
The single hardest proof in the corpus is complete, no sorry. Under the
value-equality invariant y = MTH D₁, an accepting ConsRec fold either
makes extractConsNode output a genuine collision or its first component
is the honest prefix root MTH(D₁.take n₀).

- ConsRec base changed from list-match to decidable if (if C=[] /
  if C.length=1) — same root-cause fix as Root, avoids WF-unfold
  exhaustiveness obligations; more faithful to the deployed Python.
  Whole chain (Basic..Consistency) rebuilt clean.
- consRecBinding by ConsRec.induct (10 cases): 4 base/singleton, 3
  rejection/none contradictions, 2 recursive (n₀≤k, n₀>k). The n₀>k
  none-branch is where all S5.1 infrastructure interlocks:
  kbelow_prefix_eq (prefix splits at same k) + take_take_le +
  take_drop_prefix assemble x = hnode s xx into MTH(D₁.take n₀). The
  collision branches use append_inj (fixed-width Hash) + MTH_split.
- take_all helper (take-whole-list).

Cone [propext, Classical.choice, LTLAcc.sha256, Quot.sound] — single hash
axiom. 24 certs green. Fable statement-audit: matches paper Thm 3
steps 1-2. LTL untouched (12 leaves, bcd15f9d).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-11 19:18:26 +02:00
..
AxiomCheck.lean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00
AxiomCheck.olean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00
Basic.lean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00
Basic.olean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00
Binding.olean S3/L4-L5: root binding (Lemma 2, Path instance) + Theorem 2, constructive 2026-07-11 13:21:17 +02:00
Binding3.lean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00
Binding3.olean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00
Completeness.lean S3.5: explicit collision extractor — Theorem 2 made non-vacuous, vacuous forms removed 2026-07-11 15:31:21 +02:00
Completeness.olean S3.5: explicit collision extractor — Theorem 2 made non-vacuous, vacuous forms removed 2026-07-11 15:31:21 +02:00
Consistency.lean S5 stage 2: extractConsNode extractor defined (consistency, Theorem 3 steps 1-2) 2026-07-11 17:55:51 +02:00
Consistency.olean S5 stage 2: extractConsNode extractor defined (consistency, Theorem 3 steps 1-2) 2026-07-11 17:55:51 +02:00
Descent.lean S4: descent extractor extractMTH (Theorem 3 step 3 + F2 restoration), non-vacuous 2026-07-11 16:46:58 +02:00
Descent.olean S4: descent extractor extractMTH (Theorem 3 step 3 + F2 restoration), non-vacuous 2026-07-11 16:46:58 +02:00
Extract.lean S3.5 Fable re-audit: permanent non-vacuity witness + honest ledger 2026-07-11 16:38:34 +02:00
Extract.olean S3.5 Fable re-audit: permanent non-vacuity witness + honest ledger 2026-07-11 16:38:34 +02:00
Probe.olean S3.5: explicit collision extractor — Theorem 2 made non-vacuous, vacuous forms removed 2026-07-11 15:31:21 +02:00
ProbeAx.olean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00
ProbeInduct.olean S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00