Proof step 62 from proof prepost-write-once (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 63:

  # apebs2 = # wlar0, # apebs0 = # wlar, q0.head = eq-entry(m4, lref), LEB_SIZE = (n2 + m0) + m1, apebs2[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar0[vtblpnum1] = wl-entry(m5, free), vols0[v][m] = unmapped, aehdr.valid?, vtblpnum1 < # wlar0, m < # vols0[v], bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), ubi-io-inv(apebs2), ubi-io-inv(apebs0), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false)]), unique-sqns(apebs2), unique-sqns(apebs0), valid-ebatbl(apebs2, wlar0, vols0, vtblpnum2), valid-ebatbl(apebs0, wlar, vols0, vtblpnum2), valid-eraseq(apebs2, q1), valid-eraseq(wlar0, q1), valid-eraseq(q1), valid-eraseq(q0), valid-eraseq(wlar, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs2, sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-vtbl(apebs0, vols0, wlar, vtblpnum2), valid-wl(apebs2, wlar0), valid-wl(apebs0, wlar), v ∈ vols0, m0 + m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m1 ≤ LEB_SIZE, m2 + m1 ≤ # buf, m0 ≤ LEB_SIZE, m1 + m0 ≤ LEB_SIZE, q1.lebrefs ⊆ q0.lebrefs, apebs0 = apebs2 ∧ wlar = wlar0 ∧ q0 = q1 ∨ id○(apebs0, apebs2, vtblpnum1) ∧ id○(wlar, wlar0, vtblpnum1) ∧ q0 = eq-entry(vtblpnum1, lref) ' + q1 ⊦ m1 = 0, vtblpnum2 = vtblpnum1, vtblpnum2 ∈ q1, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q0, unique-sqns (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false)]) ∧ valid-global-sqn (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false)], sqnum + 1) ∧ valid-wl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false)], wlar0[vtblpnum1, wl-entry(m5, used)]) ∧ valid-eraseq(wlar0[vtblpnum1, wl-entry(m5, used)], q1) ∧ valid-eraseq (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false)], q1) ∧ valid-ebatbl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false)], wlar0[vtblpnum1, wl-entry(m5, used)], vols0[v, vols0[v][m, ⌜vtblpnum1⌝ ]], vtblpnum2) ∧ (∃ n. vols0[v, vols0[v][m, ⌜vtblpnum1⌝ ]] = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ apebs2 [vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false) ] [n ] .fill = m0 + m1 ∧ apebs2 [vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m0 - m1), m0 + m1, false) ] [n ] .data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n2))

Rule argument

Additional information

Used simplifier rules: ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ s1 ⊆ s2 → s1 ⊆ s2 ++ lref; (s)%¬ n ∈ ns ⊦ id(apebs1[n, apeb], apebs0, ns) ↔ id(apebs1, apebs0, ns); (s)%n < # wlar, stat ≠ used ⊦ wlar[n] = wl-entry(m, stat) ∧ valid-ebatbl(apebs, wlar, vols, n0) → ¬ n ∈ mapped-pebs(vols); (s)% ⊦ used ≠ free; (s)%⊦ m ≠ n0 → ( valid-vtbl(apebs, vols, wlar[m, wle], n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)%⊦ v ∈ vols → ( valid-vtbl(apebs, vols[v, vols[v][m, ebae]], wlar, n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)%⊦ m ≠ n0 → ( valid-vtbl(apebs[m, apeb], vols, wlar, n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)%⊦ bflipset-cons(bflipset, wlar) → bflipset-cons(bflipset, wlar[m, wl-entry(n, used)]); (ss)% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ # apebs[n, apeb] = # apebs; (s)%m < # apebs ⊦ apebs[m, apeb][m, apeb0] = apebs[m, apeb0]; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ n1 ≤ n0 → subarray(mkempbuf(n0), 0, n1) = mkempbuf(n1); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (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)