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Proof step 467 from proof prepost-scan-all (previous step)

# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avhdr1, buf1, m0, false), avhdr1 = avidhdr(v, m1, m2, m3, m4), m3 = 0, valid-sqns(v, m1, apebs, vtblpnum) = ∅, avhdr1.valid?, nx < vtblpnum, bflipset-cons(bflipset0, subarray(wlar0, 0, vtblpnum)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avhdr1, 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-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)) ⊦ avhdr1 = empty, n0 = 0, dups(nx), v × m1 ∈ recs, valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, m2 + 1)) ∧ valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, used)], 0, vtblpnum + 1)) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, m2)]) ∧ valid-recs (subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, used)], 0, vtblpnum + 1), recs[v × m1, recovery-entry(vtblpnum, m2)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 468:
# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false), valid-sqns(v, m1, apebs, vtblpnum) = ∅, nx < vtblpnum, bflipset-cons(bflipset0, 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-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)) ⊦ n0 = 0, dups(nx), v × m1 ∈ recs, valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, m2 + 1)) ∧ valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, used)], 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-eraseq-stronger-notin-recs: # apebs = # wlar ⊦ valid-eraseq-stronger(apebs, q) ∧ valid-eraseq(wlar, q) ∧ valid-recs(apebs, wlar, recs) ∧ valid-wl(apebs, wlar) ∧ ¬ v × m ∈ recs → valid-sqns(v, m, apebs) = ∅;%n ≤ # apebs ⊦ valid-sqns(v, m, subarray(apebs, 0, n)) = valid-sqns(v, m, apebs, n); (s)% ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # subarray(wlar, m, n) = n; (s)% ⊦ # subarray(apebs, m, n) = n; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%m < # apebs, # wlar = # apebs ⊦ valid-recs(subarray(apebs, 0, m), subarray(wlar, 0, m), recs) ∧ apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m4), buf, m2, boolvar) ∧ ¬ v × n ∈ recs → valid-recs (subarray(apebs, 0, m + 1), subarray(wlar[m, wl-entry(m3, used)], 0, m + 1), recs[v × n, recovery-entry(m, m0)]); (ss)%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)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)% ⊦ empty ≠ avidhdr(v, m, m0, m1, m2); (s)