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Proof step 153 from proof prepost-scan-all (previous step)

# wlar0 = n1 + vtblpnum1, # apebs = n1 + vtblpnum1, avhdr.sqn = valid-sqns(v, m1, apebs, vtblpnum1).max, apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, avhdr.sqn, m3, checksum(buf1, m3)), buf1, m0, false), recs[v × m1] = recovery-entry(m4, avhdr.sqn), apebs[m4] = mkpeb(aehdr, avhdr, buf, m5, boolvar), wlar0[m4] = wl-entry(m6, stat), m4 < n1 + vtblpnum1, m4 < vtblpnum1, nx < vtblpnum1, bflipset-cons(bflipset0, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m5, boolvar)), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, avhdr.sqn, m3, checksum(buf1, m3)), buf1, m0, false)), 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, avhdr.sqn, m3, checksum(buf1, m3)), buf1, m0, false)), valid-peb(mkpeb(aechdr(m), avidhdr(v, m1, avhdr.sqn, 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 ≤ LEB_SIZE, m3 ≤ datasize(buf1), bitflips0 ∨ bitflips ⊦ m3 = 0, n1 = 0, dups(nx), m4 ∈ q, indices-erasing(wlar0[vtblpnum1, wl-entry(m, used)][m4, wl-entry(m6, erasing)], nx) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1 + 1), q + eq-entry(m4, v × m1) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum1 + 1), subarray(wlar0[vtblpnum1, wl-entry(m, used)][m4, wl-entry(m6, erasing)], 0, vtblpnum1 + 1)) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum1, avhdr.sqn)])

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: unique-sqns-2-valid-pebs seq: ⊦ m0 < # apebs ∧ m1 < # apebs ∧ valid-peb(v, m, apebs[m0]) ∧ valid-peb(v, m, apebs[m1]) ∧ unique-sqns(apebs) ∧ m0 ≠ m1 → apebs[m0].vidhdr.sqn ≠ apebs[m1].vidhdr.sqn subst: [m0, apebs, m1, v, m] → [vtblpnum1, apebs, m4, v, m1]

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%⊦ 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)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ ¬ n < n; (s)%# wlar = n ⊦ subarray(wlar, 0, n) = wlar; (s)%# apebs = n ⊦ subarray(apebs, 0, n) = apebs; (s) Used terms: vtblpnum1, apebs, m4, v, m1