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Proof step 432 from proof prepost-scan-all (previous step)

# wlar0 = n0 + vtblpnum, # apebs = n0 + vtblpnum, avhdr1.size = 0, apebs[vtblpnum] = mkpeb(aechdr(m), avhdr1, buf1, m0, false), avhdr1.valid?, nx < vtblpnum, avhdr1.sqn < recs[avhdr1.vol × avhdr1.leb].sqn, 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.vol × avhdr1.leb ∈ recs ⊦ avhdr1 = empty, n0 = 0, dups(nx), valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, avhdr1.sqn + 1)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum + 1), q + eq-entry(vtblpnum, avhdr1.vol × avhdr1.leb) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, erasing)], 0, vtblpnum + 1))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 433:
# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avhdr1, buf1, m0, false), avhdr1 = avidhdr(v, m1, m2, m3, m4), m3 = 0, avhdr1.valid?, m2 < recs[v × m1].sqn, 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)), v × m1 ∈ recs ⊦ avhdr1 = empty, n0 = 0, dups(nx), valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, m2 + 1)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum + 1), q + eq-entry(vtblpnum, v × m1) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, erasing)], 0, vtblpnum + 1))

Rule argument

spec: avidheader name: elim seq: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)) subst: [avhdr, v, m, m0, m1, m2] → [avhdr1, v, m1, m2, m3, m4]

Additional information

Used simplifier rules: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)); (elim) Used terms: avhdr1, v, m1, m2, m3, m4