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Proof step 123 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n3 + align↑(datasize(buf, n0), EB_PAGE_SIZE), LEB_SIZE = n2 + n0, LEB_SIZE = n4 + align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), wlar[vtblpnum1] = wl-entry(m0, used), wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, vtblpnum1 < # wlar, n1 < # wlar, bflipset-cons(bflipset, 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))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), 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))), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ # buf, n0 ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE) ≤ LEB_SIZE ⊦ checksum(buf, datasize(buf, n0)) = checksum(subarray(buf, 0, n0) + mkempbuf(n2), datasize(buf, n0)), vtblpnum1 = n1, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ∃ buf0. buf = mkempbuf(n0) + buf0, unique-sqns (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) ]) ∧ 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) ∧ valid-wl (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) ], wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)]) ∧ valid-eraseq(wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-eraseq (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) ], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ bflipset-cons(bflipset -- vtblpnum1, wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: checksum name: checksum-append-left seq: ⊦ n ≤ # buf0 → checksum(buf0 + buf1, n) = checksum(buf0, n) subst: [n, buf1, buf0] → [datasize(buf, n0), mkempbuf(n2), subarray(buf, 0, n0)] flags: <all paths>

Additional information

Used simplifier rules: ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < datasize(buf, n); (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # mkempbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: datasize(buf, n0), mkempbuf(n2), subarray(buf, 0, n0)