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Proof step 71 from proof prepost-scan-all (previous step)

# apebs = n0 + vtblpnum, # wlar = n0 + vtblpnum, wlar[vtblpnum] = wl-entry(m0, stat), apebs[vtblpnum] = mkpeb(aehdr0, avhdr0, buf0, m, false), nx < vtblpnum, bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum)), indices-erasing(wlar, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf0, m, false)), unique-sqns(apebs), valid-eraseq(subarray(wlar, 0, vtblpnum), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q), valid-global-sqn(subarray(apebs, 0, vtblpnum), sqnum), valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum)) ⊦ n0 = 0, aehdr0.valid?, dups(nx), valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar[vtblpnum, wl-entry(m0, erasing)], 0, vtblpnum + 1))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-wl-next-invalid-erase seq: m < # apebs, # apebs = # wlar ⊦ valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)) ∧ ¬ valid-peb(apebs[m]) → ( valid-wl (subarray(apebs, 0, m + 1), subarray(wlar[m, wl-entry(m0, erasing)], 0, m + 1)) ↔ ¬ apebs[m].bad) subst: [m0, wlar, m, apebs] → [m0, wlar, vtblpnum, apebs] flags: <all paths>

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ ¬ aehdr.valid? → ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)); (s) Used terms: m0, wlar, vtblpnum, apebs