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Proof step 225 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, m2, m3, checksum(buf1, m3)), buf1, m0, false), recs[v × m1] = recovery-entry(m4, avhdr.sqn), apebs[m4] = mkpeb(aehdr, avhdr, buf, m5, boolvar), m2 < avhdr.sqn, m4 < vtblpnum1, nx < vtblpnum1, vtblpnum1 < # apebs, bflipset-cons(bflipset, 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, m2, 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(aehdr, avhdr, buf, m5, boolvar)), valid-peb(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), buf1, m0, false)), 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) ⊦ m3 = 0, n1 = 0, dups(nx), m4 ∈ q, (valid-peb(v, m1, apebs[vtblpnum1]) ∧ apebs[vtblpnum1].vidhdr.sqn ≠ valid-sqns(v, m1, apebs, vtblpnum1 + 1).max) ∧ valid-wl(subarray(apebs, 0, vtblpnum1 + 1), subarray(wlar0[vtblpnum1, wl-entry(m, erasing)], 0, vtblpnum1 + 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ls-max: ⊦ (bag ++ n).max = (bag = ∅ ⊃ n;(bag.max > n ⊃ bag.max;n));%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)%⊦ valid-peb(apeb) → (valid-peb(v, m, apeb) ↔ v = apeb.vidhdr.vol ∧ m = apeb.vidhdr.leb); (ss)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ m +1 = m + 1; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ m > n ↔ n < m; (s)%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)% ⊦ m < m + n ↔ n ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]% ⊦ bag ∪ {n} = bag ++ n; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)%⊦ n < # apebs → valid-sqns(v, m, apebs, n + 1) = valid-sqns(v, m, apebs, n) ∪ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅); (s)