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Proof step 208 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n4 + align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), LEB_SIZE = n2 + n0, LEB_SIZE = n3 + align↑(datasize(buf, n0), EB_PAGE_SIZE), vols[v][m0] = unmapped, apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), aehdr.valid?, m0 < # vols[v], n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), ubi-io-inv (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-peb (mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, n0 ≤ LEB_SIZE, n0 ≤ # buf ⊦ vtblpnum1 = n1, valid-ebatbl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar[n1, wl-entry(m1, used)], vols[v, vols[v][m0, ⌜n1⌝ ]], vtblpnum1), vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ∃ buf0. buf = mkempbuf(n0) + buf0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 209:
n < # wlar, n < # apebs ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = unmapped ∧ n ≠ n0 ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ wlar[n].status ≠ used → (valid-ebatbl(apebs, wlar[n, wl-entry(m0, used)], vols[v, vols[v][m, ⌜n⌝ ]], n0) ↔ valid-ebatbl(apebs, wlar, vols, n0))

Rule argument

spec: ubi-base name: valid-ebatbl-map seq: n < # wlar, n < # apebs ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = unmapped ∧ n ≠ n0 ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ wlar[n].status ≠ used → ( valid-ebatbl (apebs, wlar[n, wl-entry(m0, used)], vols[v, vols[v][m, ⌜n⌝ ]], n0) ↔ valid-ebatbl(apebs, wlar, vols, n0)) subst: [n0, m, v, vols, m0, n, wlar, apebs] → [vtblpnum1, m0, v, vols, m1, n1, wlar, apebs0 [n1, mkpeb (aehdr, avidhdr (v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ # apebs[n, apeb] = # apebs; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)% ⊦ used ≠ free; (s)%stat ≠ used ⊦ wlar[m] = wl-entry(m0, stat) → ( valid-ebatbl(apebs[m, apeb], wlar, vols, n) ↔ valid-ebatbl(apebs, wlar, vols, n)); (ss)% ⊦ wl-entry(m, stat).status = stat; (s) Used terms: vtblpnum1, m0, v, vols, m1, n1, wlar, apebs0 [n1, mkpeb (aehdr, avidhdr (v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]