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Proof step 371 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(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, false), aechdr(aehdr0.ec) = aehdr0, m3 < n0 + vtblpnum, nx < vtblpnum, m3 < vtblpnum, m3 + 1 < n0 + vtblpnum, avhdr.sqn < m2, bflipset-cons(bflipset0, 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(mkpeb(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, 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-peb(mkpeb(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, false)), valid-peb(v, m1, mkpeb(aehdr0, avidhdr(v, m1, m2, 0, m4), buf0, m, false)), 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(aehdr0.ec, used)][m3, wl-entry(m6, erasing)], nx) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum, m2)])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-crash-recovery-base name: indices-set-erasing seq: ⊦ indices-erasing(wlar, nx) → indices-erasing(wlar[m, wl-entry(n, erasing)], nx) subst: [nx, n, m, wlar] → [nx, m6, m3, wlar0[vtblpnum, wl-entry(aehdr0.ec, used)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ valid-recs-sqns(apebs, recs) → ( valid-recs-sqns(apebs, recs[v × m, recovery-entry(m0, m1)]) ↔ m0 < # apebs ∧ apebs[m0].vidhdr.sqn = m1); (ss)% ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)%⊦ nx < m ∧ indices-erasing(wlar, nx) → indices-erasing(wlar[m, wle], nx); (ss) Used terms: nx, m6, m3, wlar0[vtblpnum, wl-entry(aehdr0.ec, used)]