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Proof step 24 from proof prepost-io-write-data (previous step)

# apebs = # wlar, LEB_SIZE = (n0 + m2) + m0, wlar[n] = wl-entry(m3, used), apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), avhdr.valid?, aehdr.valid?, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), ubi-io-inv(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)]), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, n2), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m2 + m0 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m ≤ m0, m ≤ LEB_SIZE ⊦ n3 = n, n ∈ q, VTBL_VOLID ∈ vols, n3 ∈ q, unique-sqns(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)]) ∧ valid-global-sqn(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)], n2) ∧ valid-wl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)], wlar) ∧ valid-eraseq(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)], q) ∧ valid-ebatbl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)], wlar, vols, n3), n < # apebs ∧ apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false) ∧ valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)) ∧ valid-peb(mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# apebs = # wlar, LEB_SIZE = (n0 + m2) + m0, wlar[n] = wl-entry(m3, used), apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), avhdr.valid?, aehdr.valid?, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), ubi-io-inv(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)]), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, n2), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m2 + m0 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m ≤ m0, m ≤ LEB_SIZE ⊦ n3 = n, valid-peb(mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)), n ∈ q, VTBL_VOLID ∈ vols, n3 ∈ q, unique-sqns(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)]) ∧ valid-wl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)], wlar) ∧ valid-ebatbl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)], wlar, vols, n3)

Rule argument

Additional information

Used simplifier rules: m < # apebs ⊦ ¬ valid-peb(apeb) ∧ valid-eraseq(apebs, q) → valid-eraseq(apebs[m, apeb], q); (ss)%m < # apebs ⊦ ¬ valid-peb(apeb) ∧ valid-global-sqn(apebs, n) → valid-global-sqn(apebs[m, apeb], n); (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]