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Proof step 405 from proof prepost-scan-all (previous step)

# wlar0 = n0 + vtblpnum, # apebs = n0 + vtblpnum, avhdr.sqn = valid-sqns(v, m1, apebs, vtblpnum).max, wlar0[m3] = wl-entry(m6, stat), apebs[m3] = mkpeb(aehdr, avhdr, buf, m5, boolvar), recs[v × m1] = recovery-entry(m3, avhdr.sqn), apebs[vtblpnum] = mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false), nx < vtblpnum, m3 < vtblpnum, m3 < n0 + vtblpnum, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false)), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m5, boolvar)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q), valid-global-sqn(subarray(apebs, 0, vtblpnum), sqnum), valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m5, boolvar)), valid-peb(mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false)), valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar0, 0, vtblpnum), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar0, 0, vtblpnum)), v × m1 ∈ recs, avhdr.sqn ≤ m2 ⊦ n0 = 0, dups(nx), m3 ∈ q, indices-erasing(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(m6, erasing)], nx) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum + 1), q + eq-entry(m3, v × m1) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(m6, erasing)], 0, vtblpnum + 1)) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, m2)]), vtblpnum < # apebs ∧ m3 < vtblpnum ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q) ∧ valid-peb(v, m1, apebs[vtblpnum]) ∧ valid-sqns(v, m1, apebs, vtblpnum).max < apebs[vtblpnum].vidhdr.sqn ∧ valid-peb(v, m1, apebs[m3]) ∧ ¬ m3 ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 406:
# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, avhdr.sqn = valid-sqns(v, m1, apebs, vtblpnum).max, apebs[vtblpnum] = mkpeb(aechdr(m), avidhdr(v, m1, avhdr.sqn, 0, m4), buf1, m0, false), recs[v × m1] = recovery-entry(m3, avhdr.sqn), apebs[m3] = mkpeb(aehdr, avhdr, buf, m5, boolvar), wlar0[m3] = wl-entry(m6, stat), m3 < n0 + vtblpnum, m3 < vtblpnum, nx < vtblpnum, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum)), 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, 0, m4), buf1, m0, false)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q), valid-global-sqn(subarray(apebs, 0, vtblpnum), sqnum), valid-peb(v, m1, mkpeb(aechdr(m), avidhdr(v, m1, avhdr.sqn, 0, m4), buf1, m0, false)), valid-peb(mkpeb(aechdr(m), avidhdr(v, m1, avhdr.sqn, 0, m4), buf1, m0, false)), valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m5, boolvar)), valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar0, 0, vtblpnum), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar0, 0, vtblpnum)), v × m1 ∈ recs ⊦ n0 = 0, dups(nx), m3 ∈ q, indices-erasing(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(m6, erasing)], nx) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum + 1), q + eq-entry(m3, v × m1) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(m6, erasing)], 0, vtblpnum + 1)) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, avhdr.sqn)])

Rule argument

Additional information

Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb);% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m ≤ m; (s)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ 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)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)