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Proof step 370 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(aehdr0.ec), avidhdr(v, m1, m2, 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), apebs[vtblpnum] = mkpeb(aehdr0, avhdr0, buf0, m, boolvar0), avhdr.sqn < m2, m3 + 1 < n0 + vtblpnum, avhdr.sqn < avhdr0.sqn, m3 < vtblpnum, nx < vtblpnum, m3 < n0 + vtblpnum, bflipset-cons(bflipset0, subarray(wlar0, 0, vtblpnum)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(apebs[vtblpnum]), 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(v, m1, apebs[vtblpnum]), valid-peb(apebs[vtblpnum]), 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(aehdr0.ec, used)][m3, wl-entry(m6, erasing)], nx) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, m2)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 371:
# 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(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, false), aechdr(aehdr0.ec) = aehdr0, m3 < n0 + vtblpnum, nx < vtblpnum, m3 < vtblpnum, m3 + 1 < n0 + vtblpnum, avhdr.sqn < m2, bflipset-cons(bflipset0, 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(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, 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(mkpeb(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, false)), valid-peb(v, m1, mkpeb(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, 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(aehdr0.ec, used)][m3, wl-entry(m6, erasing)], nx) ∧ 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);% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ m < n → n ≠ 0; (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)