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Proof step 93 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), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), wlar[vtblpnum1] = wl-entry(m0, used), aehdr.valid?, n1 < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset -- vtblpnum1, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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(VTBL_VOLID, VTBL_LNUM, 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(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-peb (mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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), 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-global-sqn (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], sqnum + 1), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, ∃ buf0. buf = mkempbuf(n0) + buf0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-global-sqn-add-valid seq: m < # apebs ⊦ valid-peb(apeb) ∧ valid-global-sqn(apebs, n) ∧ apeb.vidhdr.sqn < n → valid-global-sqn(apebs[m, apeb], n) subst: [n, apeb, m, apebs] → [sqnum + 1, mkpeb (aehdr, avidhdr (VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false), n1, apebs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ valid-global-sqn(apebs, n) → valid-global-sqn(apebs, n + m); (ss)%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)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s) Used terms: sqnum + 1, mkpeb (aehdr, avidhdr (VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false), n1, apebs0