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Proof step 168 from proof prepost-write-once (previous step)

# apebs0 = # wlar, # apebs2 = # wlar0, q0.head = eq-entry(m4, lref), apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)][vtblpnum].vidhdr.leb = m, apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)][vtblpnum].vidhdr.vol = v, LEB_SIZE = n1 + m0, wlar0[vtblpnum] = wl-entry(m5, free), apebs2[vtblpnum] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), vols0[v][m] = unmapped, aehdr.valid?, apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)][vtblpnum].vidhdr.valid?, vtblpnum < # wlar0, vtblpnum < # apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], m < # vols0[v], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs2[vtblpnum, 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-peb(mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols0, wlar, vtblpnum2), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-wl(apebs0, wlar), valid-wl(apebs2, wlar0), v ∈ vols0, m2 ≤ # buf, m0 ≤ 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 ⊦ wlar0[vtblpnum].status = used, vtblpnum = vtblpnum2, vtblpnum2 ∈ q1, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q0, unique-sqns(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]) ∧ valid-global-sqn(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], sqnum + 1) ∧ valid-wl(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar0[vtblpnum, wl-entry(m5, used)]) ∧ valid-eraseq(wlar0[vtblpnum, wl-entry(m5, used)], q1) ∧ valid-ebatbl(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar0, vols0, vtblpnum2) ∧ (∃ n. vols0[v, vols0[v][m, ⌜vtblpnum⌝ ]] = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)][n].fill = 0 ∧ apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)][n].data = mkempbuf(LEB_SIZE))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 169:
# apebs0 = # wlar, # apebs2 = # wlar0, q0.head = eq-entry(m4, lref), LEB_SIZE = n1 + m0, wlar0[vtblpnum] = wl-entry(m5, free), apebs2[vtblpnum] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), vols0[v][m] = unmapped, aehdr.valid?, m < # vols0[v], vtblpnum < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs2[vtblpnum, 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-peb(mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols0, wlar, vtblpnum2), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-wl(apebs0, wlar), valid-wl(apebs2, wlar0), v ∈ vols0, m2 ≤ # buf, m0 ≤ 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 ⊦ vtblpnum = vtblpnum2, vtblpnum2 ∈ q1, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q0, unique-sqns(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]) ∧ valid-global-sqn(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], sqnum + 1) ∧ valid-wl(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar0[vtblpnum, wl-entry(m5, used)]) ∧ valid-eraseq(wlar0[vtblpnum, wl-entry(m5, used)], q1) ∧ valid-ebatbl(apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar0, vols0, vtblpnum2) ∧ (∃ n. vols0[v, vols0[v][m, ⌜vtblpnum⌝ ]] = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)][n].fill = 0 ∧ apebs2[vtblpnum, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)][n].data = mkempbuf(LEB_SIZE))

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)% ⊦ # apebs[n, apeb] = # apebs; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)