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Proof step 68 from proof prepost-get-pebs-for-wl (previous step)

# apebs = # wlar, ¬ boolvar ↔ used-ecs(wlar) = ∅, wlar[vtblpnum0] = wl-entry(∅.max, free), wlar[m] = wl-entry(m0, free), wlar[vtblpnum] = wl-entry(m1, stat), below(free-ecs(wlar), free-ecs(wlar).min + 2 * WL_THRESHOLD) = ∅, m < # wlar, m0 < free-ecs(wlar).min + 2 * WL_THRESHOLD, vtblpnum0 < # wlar, unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs, wlar), boolvar → vtblpnum < # wlar ∧ stat = used ∧ m1 = used-ecs(wlar).min ⊦ # free-ecs(wlar) = 0, free-ecs(wlar) = ∅, vtblpnum1 = vtblpnum0, vtblpnum1 = m, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: wlarray name: below-nonempty seq: ⊦ ns ≠ ∅ ∧ n ≠ 0 → below(ns, ns.min + n) ≠ ∅ subst: [n, ns] → [2 * WL_THRESHOLD, free-ecs(wlar)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ WL_THRESHOLD = 0 ↔ false; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: 2 * WL_THRESHOLD, free-ecs(wlar)