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Proof step 43 from proof prepost-io-write-data (previous step)

# apebs = # wlar, LEB_SIZE = (n1 + n2) + m0, 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(n1), 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, subarray(buf0, 0, m0) + subarray(buf, m1, n2) + mkempbuf(n1), m0 + n2, false)), 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, m0 ≤ LEB_SIZE, n2 + 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(n1), m0 + n2, false)]) ∧ 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)

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 6

Additional information

Used simplifier rules: ⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, n, boolvar)) → # buf = LEB_SIZE; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%⊦ apebs[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar) → ( valid-ebatbl (apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)], wlar, vols, n0) ↔ valid-ebatbl(apebs, wlar, vols, n0)); (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ LEB_SIZE ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → m ≤ n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%⊦ ¬ m ∈ q → (valid-eraseq(apebs[m, apeb], q) ↔ valid-eraseq(apebs, q)); (ss)%m < # apebs, # apebs = # wlar ⊦ apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0) ∧ valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)) ∧ valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ∧ wlar[m] = wl-entry(m2, used) → ( valid-wl (apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)], wlar) ↔ valid-wl(apebs, wlar)); (ss)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # apebs ⊦ apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0) ∧ valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)) ∧ valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) → ( unique-sqns(apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]) ↔ unique-sqns(apebs)); (ss)