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Proof step 158 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), vols[v][m0] = ⌜m⌝ , wlar[m] = wl-entry(m2, used), aehdr.valid?, m < # wlar, 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(q + eq-entry(m, v × m0) '), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-peb(v, m0, apebs0[m]), 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, n1 ∈ q + eq-entry(m, v × m0) ', 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 ⊦ m = vtblpnum1, vtblpnum1 = n1, 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) '), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, m ∈ q, ∃ buf0. buf = mkempbuf(n0) + buf0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: erasequeue name: in-append seq: ⊦ n ∈ q + eq-entry(n0, lref) ' ↔ n ∈ q ∨ n = n0 subst: [lref, n0, q, n] → [v × m0, m, q, n1] flags: <all paths>

Additional information

Used simplifier rules: lf-valid-vtbl-neq-free: ⊦ wlar[m] = wl-entry(m0, free) ∧ valid-vtbl(apebs, vols, wlar, n) → n ≠ m;%lf-valid-wl-free-emptyvidhdr: n < # wlar, n < # apebs ⊦ wlar[n] = wl-entry(m, free) ∧ valid-wl(apebs, wlar) ∧ ubi-io-inv(apebs) → apebs[n].vidhdr = empty ∧ apebs[n].echdr.valid? ∧ apebs[n].fill = 0;%lf-used-valid-peb: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ apebs[n] = apeb ∧ valid-wl(apebs, wlar) → valid-peb(apeb);%ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # wlar ⊦ valid-eraseq(wlar, q) ∧ wlar[n] = wl-entry(m, free) → ¬ n ∈ q; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ ¬ valid-peb(mkpeb(aehdr, empty, buf, m, boolvar)); (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (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]% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ used ≠ free; (s) Used terms: v × m0, m, q, n1