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Proof step 307 from proof prepost-scan-all (previous step)

# apebs = n1 + vtblpnum1, # wlar0 = n1 + vtblpnum1, apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false), valid-sqns(v, m1, apebs, vtblpnum1) = ∅, nx < vtblpnum1, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum1), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q), valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum), valid-peb(v0, m5, mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false)), valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1)) ⊦ m3 = 0, n1 = 0, dups(nx), v × m1 ∈ recs, valid-global-sqn(subarray(apebs, 0, vtblpnum1 + 1), sqnum) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1 + 1), q + eq-entry(vtblpnum1, none) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum1 + 1), subarray(wlar0[vtblpnum1, wl-entry(m, erasing)], 0, vtblpnum1 + 1)), m3 ≤ datasize(buf1) ∧ m4 = checksum(buf1, m3)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: valid-peb name: valid-peb2 seq: ⊦ valid-peb(v, m, apeb) ↔ ¬ apeb.bad ∧ apeb.echdr.valid? ∧ (∃ m0, m1, m2. apeb.vidhdr = avidhdr(v, m, m0, m1, m2) ∧ ( m1 ≠ 0 → m1 ≤ datasize(apeb.data) ∧ m2 = checksum(apeb.data, m1))) subst: [apeb, m, v] → [mkpeb (aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false), m5, v0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ avidhdr(v, m, m0, m1, m2) = avidhdr(v0, m3, m4, m5, m6) ↔ v = v0 ∧ m = m3 ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ aechdr(m).valid?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%datasize-le-fwd: ⊦ m ≤ datasize(buf) → m ≤ # buf; (forward) from specification datasize%⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, n, boolvar)) → # buf = LEB_SIZE; (s) Used terms: mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false), m5, v0