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Proof step 187 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[m] = wl-entry(m2, used), vols[v][m0] = ⌜m⌝ , wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, n1 < # wlar, m0 < # vols[v], m < # 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))), 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(v, m0, 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(m, v × m0) '), valid-global-sqn(apebs0, sqnum), valid-peb(v, m0, apebs0[m]), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, 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, datasize(buf, n0) ≤ n0, datasize(buf, n0) ≤ # buf, datasize(buf, n0) ≤ LEB_SIZE ⊦ checksum(buf, datasize(buf, n0)) = checksum(subarray(buf, 0, n0), datasize(buf, n0)), m = vtblpnum1, vtblpnum1 = n1, m ∈ q, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ∃ buf0. buf = mkempbuf(n0) + buf0, 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[m, wl-entry(m2, erasing)][n1, wl-entry(m1, used)], vols[v, vols[v][m0, ⌜n1⌝ ]], vtblpnum1) ∧ bflipset-cons(bflipset -- m, wlar[m, wl-entry(m2, erasing)][n1, wl-entry(m1, used)]) ∧ valid-eraseq (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) ], q + eq-entry(m, v × m0) ') ∧ valid-eraseq(wlar[m, wl-entry(m2, erasing)][n1, wl-entry(m1, used)], q + eq-entry(m, v × m0) ') ∧ valid-wl (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[m, wl-entry(m2, erasing)][n1, wl-entry(m1, used)]) ∧ valid-global-sqn (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) ], sqnum + 1) ∧ unique-sqns (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) ])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%n2 ≤ n1 ⊦ n1 < # buf → subarray(subarray(buf, 0, n1), 0, n2) = subarray(buf, 0, n2); (s)% ⊦ subarray(buf, n0, n1) = subarray(buf, n0, n2) ↔ n1 = n2; (ss)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: buf, datasize(buf, n0), subarray(buf, 0, n0)