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Proof step 19 from proof inv-write-data (previous step)

LEB_SIZE = (n0 + n4) + n5, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), avhdr.valid?, aehdr.valid?, n < # apebs, is-aligned(n4, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), n4 + n5 ≤ LEB_SIZE, n5 ≤ LEB_SIZE, m ≤ LEB_SIZE, n1 + n4 ≤ # buf, n5 + n4 ≤ LEB_SIZE, m ≤ n5 ⊦ # mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).data = LEB_SIZE ∧ ( ¬ mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).bad → ( mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).echdr = empty → mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).vidhdr = empty) ∧ ( mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).echdr ≠ garbage ∧ mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).vidhdr = empty → mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill = 0) ∧ mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill ≤ LEB_SIZE ∧ is-aligned(mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill, EB_PAGE_SIZE) ∧ subarray (mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).data, mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill, LEB_SIZE - mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill) = mkempbuf(LEB_SIZE - mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m - m = 0; (s)% ⊦ m ≤ m; (s)% ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ ¬ n < n; (s)% ⊦ LEB_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + n; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ ¬ empty.valid?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ ¬ empty.valid?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)%⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, n, boolvar)) → # buf = LEB_SIZE; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)