mirror of
https://github.com/saymrwulf/ltl-accumulator-verified.git
synced 2026-09-04 20:03:44 +00:00
mrwulf
be232507cc
The 'descend' step of the paper's Theorem 3, built extractor-first per the S3.5 lesson (never a bare '∨ collision'): - extractMTH (D D'): total function that, given two equal-length leaf lists sharing a Merkle root, walks the common-shape tree to the first divergence and returns the concrete colliding preimage pair (a node pair, or a leaf pair at the bottom). - extractMTH_correct: |D|=|D'| ∧ D≠D' ∧ MTH D = MTH D' → IsCollision (extractMTH D D'). Proven by functional induction on extractMTH; composite case uses MTH_split + append_inj (fixed-width Hash) to split node preimages or exhibit the node collision. - extractMTH_nonvacuous: equal lists → output NOT a collision (pinned), so the conclusion is false for some inputs ⇒ choice-proof. This also RESTORES, in explicit non-vacuous form, the receipt-uniqueness content of Lemma 2 deleted in the S3.5 cleanup (re-audit F2): the honest Merkle fold is injective up to a collision. 18 certs green. Fable statement-audit passed (matches paper Thm 3 step 3 verbatim). LTL untouched (12 leaves, bcd15f9d). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
23 lines
763 B
Text
23 lines
763 B
Text
/- Axiom-cone observation for the audit (Phase 3 of check.sh). -/
|
|
import Proofs.Basic
|
|
import Proofs.Completeness
|
|
import Proofs.Extract
|
|
import Proofs.Descent
|
|
#print axioms LTLAcc.domsep
|
|
#print axioms LTLAcc.kbelow_pos
|
|
#print axioms LTLAcc.kbelow_lt
|
|
#print axioms LTLAcc.le_two_kbelow
|
|
#print axioms LTLAcc.kbelow_pow2
|
|
#print axioms LTLAcc.MTH
|
|
#print axioms LTLAcc.Root
|
|
#print axioms LTLAcc.ConsRec
|
|
#print axioms LTLAcc.Path
|
|
#print axioms LTLAcc.incl_complete
|
|
#print axioms LTLAcc.hnode_preimage_inj
|
|
#print axioms LTLAcc.IsCollision
|
|
#print axioms LTLAcc.extractIncl
|
|
#print axioms LTLAcc.extractIncl_correct
|
|
#print axioms LTLAcc.extractIncl_nonvacuous
|
|
#print axioms LTLAcc.extractMTH
|
|
#print axioms LTLAcc.extractMTH_correct
|
|
#print axioms LTLAcc.extractMTH_nonvacuous
|