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Proof step 271 from proof prepost-scan-all (previous step)

# wlar0 = n1 + vtblpnum1, # apebs = n1 + vtblpnum1, apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), buf1, m0, false), valid-sqns(v, m1, apebs, vtblpnum1) = ∅, nx < vtblpnum1, bflipset-cons(bflipset0, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), 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(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, checksum(buf1, m3)), 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 ≤ datasize(buf1), m3 ≤ LEB_SIZE, bitflips0 ∨ bitflips ⊦ m3 = 0, n1 = 0, dups(nx), v × m1 ∈ recs, valid-wl(subarray(apebs, 0, vtblpnum1 + 1), subarray(wlar0[vtblpnum1, wl-entry(m, used)], 0, vtblpnum1 + 1)) ∧ valid-recs-sqns(apebs, recs[v × m1, recovery-entry(vtblpnum1, m2)])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-wl-next-valid-use seq: m < # apebs, # apebs = # wlar ⊦ valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)) ∧ valid-peb(v, n, apebs[m]) ∧ valid-sqns(v, n, apebs, m) = ∅ → ( valid-wl (subarray(apebs, 0, m + 1), subarray(wlar[m, wl-entry(m0, used)], 0, m + 1)) ↔ apebs[m].echdr.ec = m0) subst: [v, n, m0, wlar, m, apebs] → [v, m1, m, wlar0, vtblpnum1, apebs] flags: <all paths>

Additional information

Used simplifier rules: nat-sum-leq: ⊦ m = n0 + n1 → (m ≤ n1 ↔ n0 = 0);%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ 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).echdr = aehdr; (s)% ⊦ aechdr(m).ec = m; (s)%⊦ 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 < n ↔ ¬ n ≤ m; (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)%⊦ valid-peb(apeb) → (valid-peb(v, m, apeb) ↔ v = apeb.vidhdr.vol ∧ m = apeb.vidhdr.leb); (ss)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s) Used terms: v, m1, m, wlar0, vtblpnum1, apebs