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Proof step 226 from proof prepost-scan-all (previous step)

# apebs = n1 + vtblpnum1, # wlar0 = n1 + vtblpnum1, avhdr.sqn = valid-sqns(v, m1, apebs, vtblpnum1).max, apebs[m4] = mkpeb(aehdr, avhdr, buf, m5, boolvar), recs[v × m1] = recovery-entry(m4, avhdr.sqn), apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), buf1, m0, false), m4 + 1 < n1 + vtblpnum1, nx < vtblpnum1, m4 < vtblpnum1, m2 < avhdr.sqn, m4 < n1 + vtblpnum1, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), buf1, m0, false)), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m5, boolvar)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum1), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q), valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum), valid-peb(v, m1, mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), buf1, m0, false)), valid-peb(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), buf1, m0, false)), valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m5, boolvar)), valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1)), v × m1 ∈ recs, m3 ≤ datasize(buf1), m3 ≤ LEB_SIZE ⊦ m2 = avhdr.sqn, m3 = 0, n1 = 0, dups(nx), valid-wl(subarray(apebs, 0, vtblpnum1 + 1), subarray(wlar0[vtblpnum1, wl-entry(m, erasing)], 0, vtblpnum1 + 1)), m4 ∈ q

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-wl-next-valid-erase seq: m < # apebs, # apebs = # wlar ⊦ valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)) ∧ valid-peb(v, n, apebs[m]) ∧ ( valid-sqns(v, n, apebs, m) ≠ ∅ → apebs[m].vidhdr.sqn < valid-sqns(v, n, apebs, m).max) → valid-wl (subarray(apebs, 0, m + 1), subarray(wlar[m, wl-entry(m0, erasing)], 0, m + 1)) subst: [v, n, m0, wlar, m, apebs] → [v, m1, m, wlar0, vtblpnum1, apebs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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%m < # apebs, # wlar = # apebs ⊦ valid-recs(subarray(apebs, 0, m), subarray(wlar, 0, m), recs) ∧ valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)) ∧ v × n ∈ recs → valid-sqns(v, n, apebs, m) ≠ ∅; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s) Used terms: v, m1, m, wlar0, vtblpnum1, apebs