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Proof step 74 from proof refine-write-data-wl (previous step)

pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, buf0, 0, false), err = err0, m = 2 * EB_PAGE_SIZE, m0 = m1, n = align↑(datasize(buf, n), EB_PAGE_SIZE), n0 = n, n1 = 0, avhdr.valid?, aehdr.valid?, m1 < # pebs, m1 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf0, 0, false)), is-aligned(n, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n ≤ # buf, n ≤ LEB_SIZE, ⌊err0⌋ ∨ err0 = ESUCCESS, n2 < n0 ∨ n2 = 0 ∧ n0 = 0 ⊦ ⟪pebs[m0].data := copy(buf, n1, pebs[m0].data, m, n2); pebs[m0].fill := m + n2⟫ ⟨aubi_io_write_data_wl#(m1, n, buf; apebs; err1)⟩ (abs(pebs, apebs) ∧ err = err1), datasize(buf, n) = 0, err = ESUCCESS, n2 = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 75:
apebs[m1] = mkpeb(aehdr, avhdr, buf0, 0, false), pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), err = err0, m = 2 * EB_PAGE_SIZE, m0 = m1, n = align↑(datasize(buf, n), EB_PAGE_SIZE), n0 = n, n1 = 0, aehdr.valid?, avhdr.valid?, m0 < # pebs, m1 < # apebs, m1 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf0, 0, false)), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n1 + n2 ≤ # buf, m + n2 ≤ # pebs[m0].data, n ≤ LEB_SIZE, n ≤ # buf, n2 < n0 ∨ n2 = 0 ∧ n0 = 0, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪pebs := pebs[m0, pebs[m0].data:= copy(buf, n1, pebs[m0].data, m, n2)] [m0, pebs[m0, pebs[m0].data:= copy(buf, n1, pebs[m0].data, m, n2)][m0].fill:= (m + n2) ]⟫ ⟨aubi_io_write_data_wl#(m1, n, buf; apebs; err1)⟩ (abs(pebs, apebs) ∧ err = err1), datasize(buf, n) = 0, err = ESUCCESS, n2 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0, is-aligned(m, n) ⊦ m < align↑(m0, n) ↔ m < m0; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ mkpeb(buf, m, boolvar).data = buf; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # pebs ⊦ pebs[n] = mkpeb(buf, m, boolvar) ∧ mtd-cons(pebs) → # buf = PEB_SIZE; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < LEB_SIZE → ¬ PEB_SIZE < m + 2 * EB_PAGE_SIZE; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)