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Proof step 109 from proof refine-write (previous step)

# apebs0 = # wlar, # apebs = # wlar, apebs0[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), vols[v][vtblpnum3] = ⌜n4⌝ , avols[v][vtblpnum3] = mapped(buf2, m), wlar[n4] = wl-entry(m1, used), apebs = apebs0 [vtblpnum0, mkpeb (apebs0[vtblpnum0].echdr, apebs0[vtblpnum0].vidhdr, subarray(apebs0[vtblpnum0].data, 0, vtblpnum) + subarray(buf, n1, n2) + mkempbuf(LEB_SIZE - vtblpnum - n2), vtblpnum + n2, apebs0[vtblpnum0].bad) ], err = err0, n0 = n, n1 = n3, vtblpnum = vtblpnum5, vtblpnum0 = vols[v][vtblpnum3].pnum, aehdr.valid?, avhdr.valid?, vtblpnum0 < # apebs0, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n4 < # wlar, abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(apebs, q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs0, wlar), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, n1 + n2 ≤ # buf, 0 + vtblpnum ≤ # apebs0[vtblpnum0].data, vtblpnum5 + n ≤ LEB_SIZE, n3 + n ≤ # buf, n + n3 ≤ # buf, m ≤ vtblpnum5, m0 ≤ vtblpnum5, LEB_SIZE ≥ vtblpnum, LEB_SIZE - vtblpnum ≥ n2, ⌊err0⌋ ∨ err0 = ESUCCESS, n2 < n0 ∨ n2 = 0 ∧ n0 = 0 ⊦ ⟪debug#("ubi: failed to write to PEB " + vols[v][vtblpnum3].pnum.toString); let buf1 = mkbuf(vtblpnum5 + n), bitflips = ? in {aubi_io_read_data#(vols[v][vtblpnum3].pnum, 0, 0, vtblpnum5, apebs; buf1; bitflips, err); if err = ESUCCESS then {buf1 := copy(buf, n3, buf1, vtblpnum5, n); debug#("ubi: moving data from PEB " + vols[v][vtblpnum3].pnum.toString); ubi_change#(v, vtblpnum3, vtblpnum5 + n, buf1, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs; err)} else debug#("ubi: failed to read data from PEB " + vols[v][vtblpnum3].pnum.toString)}⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n, buf; avols; err1)⟩ (abs(avols, apebs, vols, q) ∧ err = err1), vols[v][vtblpnum3] = unmapped, err = ESUCCESS, n = 0, n2 = 0, vtblpnum4 = n4, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lf-mapped-in-apebs: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → n < # apebs;% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)%⊦ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, n) ∧ ebm-cons(avols) → # buf = LEB_SIZE; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%⊦ m ≠ n0 → ( valid-vtbl(apebs[m, apeb], vols, wlar, n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ ⌜m⌝ .pnum = m; (s)% ⊦ unmapped ≠ ⌜m⌝ ; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ m < n → n ≠ 0; (s)%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)% ⊦ # apebs[n, apeb] = # apebs; (s)