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Proof step 19 from proof prepost-io-write-data (previous step)

# apebs = # wlar, LEB_SIZE - m0 = n0 + m2, 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), m0 ≤ LEB_SIZE, m2 + m0 ≤ LEB_SIZE, m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m ≤ m0, m ≤ LEB_SIZE, m2 ≤ LEB_SIZE - m0 ⊦ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# apebs = # wlar, LEB_SIZE - m0 = n0 + m2, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), wlar[n] = wl-entry(m3, used), aehdr.valid?, avhdr.valid?, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(m2, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-inv(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(n0), m0 + m2, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, n2), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m ≤ LEB_SIZE, m ≤ m0, m1 + m2 ≤ # buf, m0 + m2 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m2 + m0 ≤ LEB_SIZE ⊦ n3 = n, n3 ∈ q, VTBL_VOLID ∈ vols, n ∈ 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)

Rule argument

Additional information

Used simplifier rules: n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)