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Proof step 161 from proof prepost-write-once (previous step)

# apebs2 = # wlar0, # apebs0 = # wlar, q0.head = eq-entry(m4, lref), LEB_SIZE = (n1 + m0) + m1, apebs2[vtblpnum] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar0[vtblpnum] = wl-entry(m5, free), vols0[v][m] = unmapped, apebs = apebs2, apebs1 = apebs[vtblpnum, apebs[vtblpnum].vidhdr:= avidhdr(v, m, sqnum, 0, 0)], err = ESUCCESS, err = err0, m1 = 0, vols = vols0, aehdr.valid?, m < # vols[v], vtblpnum < # apebs, vtblpnum < # 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(apebs[vtblpnum, apebs[vtblpnum].vidhdr:= avidhdr(v, m, sqnum, 0, 0)]), 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 ∈ vols, v ∈ vols0, m0 + m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m1 ≤ LEB_SIZE, q1.lebrefs ⊆ q0.lebrefs, apebs0 = apebs2 ∧ wlar = wlar0 ∧ q0 = q1 ∨ id○(apebs0, apebs2, vtblpnum) ∧ id○(wlar, wlar0, vtblpnum) ∧ q0 = eq-entry(vtblpnum, lref) ' + q1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ vtblpnum2 = vtblpnum, vtblpnum2 ∈ q0, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q1, # apebs1 = # wlar0[vtblpnum, wl-entry(wlar0[vtblpnum].ec, used)] ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum + 1) ∧ valid-wl(apebs1, wlar0[vtblpnum, wl-entry(wlar0[vtblpnum].ec, used)]) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0[vtblpnum, wl-entry(wlar0[vtblpnum].ec, used)], q1) ∧ valid-eraseq(apebs1, q1) ∧ ¬ VTBL_VOLID ∈ vols[v, vols[v][m, ⌜vtblpnum⌝ ]] ∧ bflipset-cons(bflipset, wlar0[vtblpnum, wl-entry(wlar0[vtblpnum].ec, used)]) ∧ valid-ebatbl(apebs1, wlar0[vtblpnum, wl-entry(wlar0[vtblpnum].ec, used)], vols[v, vols[v][m, ⌜vtblpnum⌝ ]], vtblpnum2) ∧ valid-vtbl(apebs1, vols[v, vols[v][m, ⌜vtblpnum⌝ ]], wlar0[vtblpnum, wl-entry(wlar0[vtblpnum].ec, used)], vtblpnum2) ∧ ubi-io-inv(apebs1) ∧ id(apebs1, apebs0, mapped-pebs(vols0)) ∧ q1.lebrefs ⊆ q0.lebrefs ++ (v × m) ∧ (m1 = 0 → q1.lebrefs ⊆ q0.lebrefs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err ≠ ESUCCESS → vols[v, vols[v][m, ⌜vtblpnum⌝ ]] = vols0) ∧ ( err = ESUCCESS → (∃ n. vols[v, vols[v][m, ⌜vtblpnum⌝ ]] = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → apebs1[n].fill = m0 + m1) ∧ (m1 = 0 → apebs1[n].fill = 0) ∧ apebs1[n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n1)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lf-valid-wl-free-emptyvidhdr: n < # wlar, n < # apebs ⊦ wlar[n] = wl-entry(m, free) ∧ valid-wl(apebs, wlar) ∧ ubi-io-inv(apebs) → apebs[n].vidhdr = empty ∧ apebs[n].echdr.valid? ∧ apebs[n].fill = 0;% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ wl-entry(m, stat).ec = m; (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr:= avhdr0 = mkpeb(aehdr, avhdr0, buf, m, boolvar); (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkempbuf(n0) + mkempbuf(n1) = mkempbuf(n0 + n1); (s)% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (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)% ⊦ # apebs[n, apeb] = # apebs; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ 0 ≤ m; (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)