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Proof step 27 from proof inv-write-data (previous step)

apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), aehdr.valid?, avhdr.valid?, n < # apebs, n2 < n4, is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(n4, EB_PAGE_SIZE), ubi-io-inv(apebs), 0 + n5 ≤ # apebs[n].data, n1 + n2 ≤ # buf, m ≤ n5, n5 + n4 ≤ LEB_SIZE, n1 + n4 ≤ # buf, LEB_SIZE - n5 ≥ n2, LEB_SIZE ≥ n5, ⌊err0⌋ ⊦ n2 = 0, ubi-io-inv (apebs [n, mkpeb (apebs[n].echdr, apebs[n].vidhdr, subarray(apebs[n].data, 0, n5) + subarray(buf, n1, n2) + mkempbuf(LEB_SIZE - n5 - n2), n5 + n2, apebs[n].bad) ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), aehdr.valid?, avhdr.valid?, n < # apebs, n2 < n4, is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(n4, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), n1 + n2 ≤ # buf, m ≤ n5, n5 + n4 ≤ LEB_SIZE, n1 + n4 ≤ # buf, n2 + n5 ≤ LEB_SIZE, m ≤ LEB_SIZE, n5 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n2 = 0, ubi-io-peb-inv(mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n2) + mkempbuf(LEB_SIZE - n5 - n2), n5 + n2, false))

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)%⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, n, boolvar)) → # buf = LEB_SIZE; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%⊦ ubi-io-inv(apebs) → ( ubi-io-inv(apebs[n, apeb]) ↔ n < # apebs ∧ ubi-io-peb-inv(apebs[n]) → ubi-io-peb-inv(apeb)); (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)