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Proof step 88 from proof prepost-write-once (previous step)

# apebs2 = # wlar0, # apebs0 = # wlar, q0.head = eq-entry(m4, lref), LEB_SIZE = (n0 + m1) + m0, 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(n0), 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(n0), m0 + m1, false)]) ∧ valid-global-sqn (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)], sqnum + 1) ∧ valid-wl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), 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(n0), m0 + m1, false)], q1) ∧ valid-ebatbl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), 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(n0), m0 + m1, false)][n].fill = m0 + m1 ∧ apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)][n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0)), ¬ mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false).bad ∧ mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false).echdr.valid? ∧ (∃ m3, m5, m4. mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false).vidhdr = avidhdr(v, m, m3, m5, m4) ∧ ( m5 ≠ 0 → m5 ≤ datasize(mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false).data) ∧ m4 = checksum(mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false).data, m5)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 89:
# apebs0 = # wlar, # apebs2 = # wlar0, q0.head = eq-entry(m4, lref), LEB_SIZE = (n0 + m1) + m0, vols0[v][m] = unmapped, wlar0[vtblpnum1] = wl-entry(m5, free), apebs2[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, m < # vols0[v], vtblpnum1 < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)]), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), ubi-io-inv(apebs2), unique-sqns(apebs0), unique-sqns(apebs2), valid-ebatbl(apebs0, wlar, vols0, vtblpnum2), valid-ebatbl(apebs2, wlar0, vols0, vtblpnum2), valid-eraseq(apebs0, q0), valid-eraseq(wlar, q0), valid-eraseq(q0), valid-eraseq(q1), valid-eraseq(wlar0, q1), valid-eraseq(apebs2, q1), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs2, sqnum), valid-vtbl(apebs0, vols0, wlar, vtblpnum2), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-wl(apebs0, wlar), valid-wl(apebs2, wlar0), v ∈ vols0, m1 + m0 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m2 + m1 ≤ # buf, m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m0 + m1 ≤ 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 ∈ q0, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q1, ∃ m3, m6, m7. avidhdr(v, m, sqnum, 0, 0) = avidhdr(v, m, m3, m6, m7) ∧ (m6 ≠ 0 → m6 ≤ datasize(mkempbuf(m0) + subarray(buf, m2, m1)) ∧ m7 = checksum(mkempbuf(m0) + subarray(buf, m2, m1), m6)), unique-sqns(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)]) ∧ valid-global-sqn (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)], sqnum + 1) ∧ valid-wl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), 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(n0), m0 + m1, false)], q1) ∧ valid-ebatbl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), 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(n0), m0 + m1, false)][n].fill = m0 + m1 ∧ apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)][n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0))

Rule argument

Additional information

Used simplifier rules: ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%⊦ avidhdr(v, m, m0, m1, m2) = avidhdr(v0, m3, m4, m5, m6) ↔ v = v0 ∧ m = m3 ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)