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Proof step 508 from proof prepost-scan-all (previous step)

# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avhdr1, buf1, m0, false), nx < vtblpnum, bflipset-cons(bflipset, 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, avhdr1.valid?, dups(nx), valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), sqnum) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum + 1), q + eq-entry(vtblpnum, none) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, erasing)], 0, vtblpnum + 1))

User applied rule case distinction

And obtained the following new goals

Proof step 509:
# wlar0 = n0 + vtblpnum, # apebs = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avhdr1, buf1, m0, false), nx < vtblpnum, bflipset-cons(bflipset, 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, avhdr1.valid?, dups(nx), valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, erasing)], 0, vtblpnum + 1))

Rule argument

pos: right 5

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m < # apebs ⊦ valid-eraseq-stronger(subarray(apebs, 0, m), q) → ( valid-eraseq-stronger (subarray(apebs, 0, m + 1), q + eq-entry(m, none) ') ↔ ¬ valid-peb(apebs[m])); (ss)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ ¬ avhdr.valid? → ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)); (s)%m < # apebs ⊦ valid-global-sqn(subarray(apebs, 0, m), n) → ( valid-global-sqn(subarray(apebs, 0, m + 1), n) ↔ ¬ valid-peb(apebs[m]) ∨ apebs[m].vidhdr.sqn < n); (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)