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Proof step 412 from proof prepost-scan-all (previous step)

# 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(aechdr(apebs[vtblpnum].echdr.ec), avidhdr(v, m1, m2, 0, m4), buf1, m0, false), m3 < n0 + vtblpnum, nx < vtblpnum, m3 < vtblpnum, avhdr.sqn < apebs[vtblpnum].vidhdr.sqn, m3 + 1 < n0 + vtblpnum, avhdr.sqn < m2, bflipset-cons(bflipset, 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(apebs[vtblpnum]), 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(apebs[vtblpnum]), valid-peb(v, m1, apebs[vtblpnum]), 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(apebs[vtblpnum].echdr.ec, used)][m3, wl-entry(m6, erasing)], nx) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, m2)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 413:
# 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(bflipset, 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)])

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[vtblpnum], aehdr0, avhdr0, buf0, m, boolvar0]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[vtblpnum], aehdr0, avhdr0, buf0, m, boolvar0