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Proof step 353 from proof prepost-scan-all (previous step)

# wlar0 = n0 + vtblpnum, # apebs = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false), recs[v × m1].pnum < n0 + 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)), v × m1 ∈ recs, recs[v × m1].sqn ≤ m2 ⊦ n0 = 0, dups(nx), indices-erasing (wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum].ec, erasing)], nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, m2 + 1)) ∧ valid-eraseq (subarray (wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum].ec, erasing)], 0, vtblpnum + 1), q + eq-entry(recs[v × m1].pnum, v × m1) ') ∧ bflipset-cons ((bflipset0 ++ vtblpnum) -- recs[v × m1].pnum, subarray (wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum].ec, erasing)], 0, vtblpnum + 1)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum + 1), q + eq-entry(recs[v × m1].pnum, v × m1) ') ∧ valid-wl (subarray(apebs, 0, vtblpnum + 1), subarray (wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum].ec, erasing)], 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)][recs[v × m1].pnum, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][recs[v × m1].pnum].ec, erasing)], 0, vtblpnum + 1), recs[v × m1, recovery-entry(vtblpnum, m2)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 354:
# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false), recs[v × m1] = recovery-entry(m3, m5), nx < vtblpnum, m3 < n0 + 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)), v × m1 ∈ recs, m5 ≤ m2 ⊦ n0 = 0, dups(nx), indices-erasing(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][m3].ec, erasing)], nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum + 1), max(sqnum, m2 + 1)) ∧ valid-eraseq (subarray(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][m3].ec, erasing)], 0, vtblpnum + 1), q + eq-entry(m3, v × m1) ') ∧ bflipset-cons ((bflipset0 ++ vtblpnum) -- m3, subarray(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][m3].ec, erasing)], 0, vtblpnum + 1)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum + 1), q + eq-entry(m3, v × m1) ') ∧ valid-wl (subarray(apebs, 0, vtblpnum + 1), subarray(wlar0[vtblpnum, wl-entry(m, used)][m3, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][m3].ec, erasing)], 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)][m3, wl-entry(wlar0[vtblpnum, wl-entry(m, used)][m3].ec, erasing)], 0, vtblpnum + 1), recs[v × m1, recovery-entry(vtblpnum, m2)])

Rule argument

spec: recovery-entry name: elim seq: ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0) subst: [rec, m, m0] → [recs[v × m1], m3, m5]

Additional information

Used simplifier rules: ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0); (elim) Used terms: recs[v × m1], m3, m5