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Proof step 72 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), 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) ])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 73:
# apebs0 = # wlar, LEB_SIZE = n4 + align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), LEB_SIZE = n2 + n0, LEB_SIZE = n3 + align↑(datasize(buf, n0), EB_PAGE_SIZE), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), wlar[vtblpnum1] = wl-entry(m0, stat), aehdr.valid?, n1 < # wlar, vtblpnum1 < # 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))), mkempbuf(LEB_SIZE), 0, 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))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, n0 ≤ LEB_SIZE, n0 ≤ # buf ⊦ vtblpnum1 = n1, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, ∃ 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(m0, 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(m0, 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(m0, 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(m0, erasing)][n1, wl-entry(m1, used)], n1)) ∧ bflipset-cons(bflipset -- vtblpnum1, wlar[vtblpnum1, wl-entry(m0, 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(m0, 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(m0, 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

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[vtblpnum1], m0, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[vtblpnum1], m0, stat