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Proof step 399 from proof prepost-scan-all (previous step)

# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, avhdr.sqn = valid-sqns(v, m1, apebs, vtblpnum).max, apebs[vtblpnum] = mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false), recs[v × m1] = recovery-entry(m3, valid-sqns(v, m1, apebs, vtblpnum).max), apebs[m3] = mkpeb(aehdr, avhdr, buf, m5, boolvar), 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(aechdr(m), avidhdr(v, m1, m2, 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, apebs[m3]), 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, valid-sqns(v, m1, apebs, vtblpnum).max ≤ m2 ⊦ n0 = 0, dups(nx), m3 ∈ q, indices-erasing(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(wlar0[m3].ec, erasing)], nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, m2 + 1)) ∧ 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(wlar0[m3].ec, erasing)], 0, vtblpnum + 1)) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, m2)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 400:
# wlar0 = n0 + vtblpnum, # apebs = n0 + vtblpnum, avhdr.sqn = valid-sqns(v, m1, apebs, vtblpnum).max, 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-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(wlar0[m3].ec, erasing)], nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, m2 + 1)) ∧ 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(wlar0[m3].ec, erasing)], 0, vtblpnum + 1)) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, m2)])

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);%lf-valid-recs-max: m ≤ # apebs, # apebs = # wlar ⊦ valid-recs(subarray(apebs, 0, m), subarray(wlar, 0, m), recs) ∧ valid-recs-sqns(apebs, recs) ∧ valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)) ∧ v × n ∈ recs ∧ recs[v × n] = recovery-entry(m0, m1) → m1 = valid-sqns(v, n, apebs, m).max;%lf-valid-recs-sqns-vidhdr: ⊦ v × m ∈ recs ∧ recs[v × m] = recovery-entry(n0, n1) ∧ valid-recs-sqns(apebs, recs) → apebs[n0].vidhdr.sqn = n1;% ⊦ 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; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)