mrwulf 6a7d93ccb7 S5 stage 1: consistency infrastructure (kbelow prefix-split + list surgery) ...

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>

2026-07-11 17:53:43 +02:00

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