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Proof step 193 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n3 + align↑(datasize(buf, n0), EB_PAGE_SIZE), LEB_SIZE = n2 + n0, LEB_SIZE = n4 + align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), vols[v][vtblpnum3] = unmapped, q0 = q, vols0 = vols, vtblpnum0 = vtblpnum1, vtblpnum2 = n1, vtblpnum3 = m0, aehdr.valid?, vtblpnum2 < # wlar, n1 < # wlar, vtblpnum3 < # vols[v], bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ # buf, n0 ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE) ≤ LEB_SIZE, v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ vtblpnum1 = n1, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, ∃ buf0. buf = mkempbuf(n0) + buf0, v = VTBL_VOLID ∧ m0 = VTBL_LNUM, # apebs0 = # wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)] ∧ unique-sqns (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]) ∧ valid-global-sqn (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], sqnum + 1) ∧ valid-wl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)]) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)], q) ∧ valid-eraseq (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], q) ∧ ¬ VTBL_VOLID ∈ vols[v, vols[v][vtblpnum3, ⌜vtblpnum2⌝ ]] ∧ bflipset-cons(bflipset, wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)]) ∧ ( v ∈ vols0 ∨ is-encoded(to-vtbl(vols0), subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)], vols[v, vols[v][vtblpnum3, ⌜vtblpnum2⌝ ]], vtblpnum0) ∧ valid-vtbl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], vols[v, vols[v][vtblpnum3, ⌜vtblpnum2⌝ ]], wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)], vtblpnum0)) ∧ ( v = VTBL_VOLID ∧ m0 = VTBL_LNUM → (∀ v0, m. ¬ v0 ∈ vols0 ∧ is-encoded(to-vtbl(vols0)[v0, m], subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, LEB_SIZE), checksum(buf, datasize(buf, LEB_SIZE))), subarray(buf, 0, LEB_SIZE), align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), false) ], wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)], vols[v, vols[v][vtblpnum3, ⌜vtblpnum2⌝ ]][v0, fill(mkebatbl(m), unmapped)], vtblpnum0) ∧ valid-vtbl (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, LEB_SIZE), checksum(buf, datasize(buf, LEB_SIZE))), subarray(buf, 0, LEB_SIZE), align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), false) ], vols[v, vols[v][vtblpnum3, ⌜vtblpnum2⌝ ]][v0, fill(mkebatbl(m), unmapped)], wlar[vtblpnum2, wl-entry(wlar[vtblpnum2].ec, used)], vtblpnum0))) ∧ (v ∈ vols0 ∧ vols0[v][m0] ≠ unmapped → q = q0 + eq-entry(vols0[v][m0].pnum, v × m0) ') ∧ (v = VTBL_VOLID ∧ m0 = VTBL_LNUM → q = q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ id (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], apebs0, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m0 = VTBL_LNUM → vols[v, vols[v][vtblpnum3, ⌜vtblpnum2⌝ ]] = vols0) ∧ (v ∈ vols0 → vols[v, vols[v][vtblpnum3, ⌜vtblpnum2⌝ ]] = vols0[v, vols0[v][m0, ⌜n1⌝ ]]) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 194:
# apebs0 = # wlar, LEB_SIZE = n3 + align↑(datasize(buf, n0), EB_PAGE_SIZE), LEB_SIZE = n2 + n0, LEB_SIZE = n4 + align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), vols[v][m0] = unmapped, aehdr.valid?, n1 < # wlar, m0 < # vols[v], bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ # buf, n0 ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE) ≤ LEB_SIZE ⊦ vtblpnum1 = n1, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, ∃ buf0. buf = mkempbuf(n0) + buf0, unique-sqns (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]) ∧ valid-global-sqn (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], sqnum + 1) ∧ valid-wl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar[n1, wl-entry(m1, used)]) ∧ valid-eraseq(wlar[n1, wl-entry(m1, used)], q) ∧ valid-eraseq (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], q) ∧ valid-ebatbl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar[n1, wl-entry(m1, used)], vols[v, vols[v][m0, ⌜n1⌝ ]], vtblpnum1)

Rule argument

Additional information

Used simplifier rules: ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ s0 ⊆ s0 ++ lref; (s)% ⊦ id(apebs, apebs, ns); (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)