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Proof step 71 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), lref = VTBL_VOLID × VTBL_LNUM, q0 = q, vtblpnum = vtblpnum1, aehdr.valid?, n1 < # wlar[vtblpnum, wlar[vtblpnum].status:= erasing], vtblpnum < # wlar, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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(VTBL_VOLID, VTBL_LNUM, 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), 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, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ∃ buf0. buf = mkempbuf(n0) + buf0, # apebs0 = # wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)] ∧ unique-sqns (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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(VTBL_VOLID, VTBL_LNUM, 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(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)]) ∧ valid-eraseq(q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-eraseq (wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)], q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-eraseq (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ bflipset-cons (bflipset -- vtblpnum1, wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)]) ∧ ( is-encoded(to-vtbl(vols), 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[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)], vols, n1) ∧ 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, wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)], n1)) ∧ (∀ v0, m. ¬ v0 ∈ vols ∧ is-encoded(to-vtbl(vols)[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[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)], vols[v0, fill(mkebatbl(m), unmapped)], n1) ∧ 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[v0, fill(mkebatbl(m), unmapped)], wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1, wl-entry(wlar[vtblpnum, wlar[vtblpnum].status:= erasing][n1].ec, used)], n1)) ∧ q + eq-entry(vtblpnum, lref) = q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ' ∧ id (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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(vols))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
# 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), aehdr.valid?, vtblpnum1 < # wlar, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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(VTBL_VOLID, VTBL_LNUM, 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-eraseq(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), 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, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ∃ buf0. buf = mkempbuf(n0) + buf0, ( ¬ v ∈ vols ∧ is-encoded(to-vtbl(vols)[v, 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[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], vols[v, fill(mkebatbl(m), unmapped)], n1) ∧ 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, fill(mkebatbl(m), unmapped)], wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], n1)) ∧ ( is-encoded(to-vtbl(vols), 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[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], vols, n1) ∧ 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, wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], n1)) ∧ bflipset-cons(bflipset -- vtblpnum1, wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)]) ∧ valid-eraseq (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-eraseq(wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-wl (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)]) ∧ valid-global-sqn (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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) ∧ unique-sqns (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ])

Rule argument

Additional information

Used simplifier rules: ⊦ eq-entry(m, lref).pnum = m; (s)% ⊦ valid-eraseq(q + eqent ') ↔ ¬ eqent.pnum ∈ q ∧ valid-eraseq(q); (ss)% ⊦ wl-entry(m, stat).ec = m; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ 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)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ q + q0 = q + q1 ↔ q0 = q1; (s)% ⊦ q + eqent = q + eqent '; (s)% ⊦ m ≠ n → wlar[n, wle][m] = wlar[m]; (s)% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ wle.status:= stat = wl-entry(wle.ec, stat); (s)