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Proof step 33 from proof prepost-io-write-data (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), wlar[n] = wl-entry(m3, used), aehdr.valid?, avhdr.valid?, n2 < m2, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n2, EB_PAGE_SIZE), 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, n2) + mkempbuf(LEB_SIZE - m0 - n2), m0 + n2, 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, n0), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m ≤ LEB_SIZE, m1 + n2 ≤ # buf, m ≤ m0, m1 + m2 ≤ # buf, m0 + m2 ≤ LEB_SIZE, n2 + m0 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n2 = 0, n3 = n, n3 ∈ q, VTBL_VOLID ∈ vols, n ∈ q, unique-sqns(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(LEB_SIZE - m0 - n2), m0 + n2, false)]) ∧ valid-global-sqn(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(LEB_SIZE - m0 - n2), m0 + n2, false)], n0) ∧ valid-wl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(LEB_SIZE - m0 - n2), m0 + n2, false)], wlar) ∧ valid-eraseq(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(LEB_SIZE - m0 - n2), m0 + n2, false)], q) ∧ valid-ebatbl (apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(LEB_SIZE - m0 - n2), m0 + n2, false)], wlar, vols, n3)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
# apebs = # wlar, LEB_SIZE - m0 = n1 + n2, wlar[n] = wl-entry(m3, used), apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), avhdr.valid?, aehdr.valid?, n < # wlar, n2 < m2, bflipset-cons(bflipset, wlar), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), ubi-io-inv(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(n1), m0 + n2, 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, n0), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m0 ≤ LEB_SIZE, n2 + m0 ≤ LEB_SIZE, m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m ≤ m0, m1 + n2 ≤ # buf, m ≤ LEB_SIZE, n2 ≤ LEB_SIZE - m0, ⌊err0⌋ ⊦ n2 = 0, n3 = n, n ∈ q, VTBL_VOLID ∈ vols, n3 ∈ q, unique-sqns(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(n1), m0 + n2, false)]) ∧ valid-global-sqn(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(n1), m0 + n2, false)], n0) ∧ valid-wl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(n1), m0 + n2, false)], wlar) ∧ valid-eraseq(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(n1), m0 + n2, false)], q) ∧ valid-ebatbl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(n1), m0 + n2, false)], wlar, vols, n3)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE - m0, n2, n1]

Additional information

Used simplifier rules: ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;% ⊦ # mkempbuf(n) = n; (s)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE - m0, n2, n1