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mrwulf
6a7d93ccb7
Theorem 3's binding (steps 1-2) turns on one non-obvious arithmetic fact, isolated and proven here before the main proof: - pow2_exp_unique / kbelow_eq_of_pow2_between: kbelow is pinned by its three defining inequalities (power-of-two, k<n≤2k), so a prefix that spills past the left subtree splits at the SAME point. - kbelow_prefix_eq: with k=kbelow n, 2≤n, k<n₀≤n ⇒ kbelow n₀ = k (the fact the n₀>k recursion branch needs to align MTH(D₁.take n₀) with the fold). - take_take_le, take_drop_prefix: the list-surgery identities relating (D.take n₀) to D.take k and (D.drop k).take (n₀-k). Cones pinned; 21 certs green. Deliberate honest checkpoint — binding + extractCons assembly is the next stage. LTL untouched. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
27 lines
899 B
Text
27 lines
899 B
Text
/- Axiom-cone observation for the audit (Phase 3 of check.sh). -/
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import Proofs.Basic
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import Proofs.Completeness
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import Proofs.Extract
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import Proofs.Descent
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import Proofs.Consistency
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#print axioms LTLAcc.domsep
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#print axioms LTLAcc.kbelow_pos
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#print axioms LTLAcc.kbelow_lt
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#print axioms LTLAcc.le_two_kbelow
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#print axioms LTLAcc.kbelow_pow2
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#print axioms LTLAcc.MTH
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#print axioms LTLAcc.Root
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#print axioms LTLAcc.ConsRec
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#print axioms LTLAcc.Path
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#print axioms LTLAcc.incl_complete
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#print axioms LTLAcc.hnode_preimage_inj
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#print axioms LTLAcc.IsCollision
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#print axioms LTLAcc.extractIncl
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#print axioms LTLAcc.extractIncl_correct
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#print axioms LTLAcc.extractIncl_nonvacuous
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#print axioms LTLAcc.extractMTH
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#print axioms LTLAcc.extractMTH_correct
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#print axioms LTLAcc.extractMTH_nonvacuous
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#print axioms LTLAcc.kbelow_prefix_eq
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#print axioms LTLAcc.take_take_le
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#print axioms LTLAcc.take_drop_prefix
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