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Proof step 359 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[vtblpnum1] = wl-entry(m0, used), aehdr.valid?, n1 < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset -- vtblpnum1, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs0, sqnum + 1), valid-global-sqn(apebs0, sqnum), valid-peb(mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ LEB_SIZE ⊦ vtblpnum1 = n1, valid-wl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)]), vtblpnum1 ∈ q, VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 360:
n < # apebs, # apebs = # wlar ⊦ valid-wl(apebs, wlar) ∧ valid-peb(apeb) ∧ (valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs) ≠ ∅ → apeb.vidhdr.sqn > valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs).max) ∧ (∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ apeb.vidhdr.vol ∨ apebs[m].vidhdr.leb ≠ apeb.vidhdr.leb) ∧ apeb.echdr.ec = m0 → valid-wl(apebs[n, apeb], wlar[n, wl-entry(m0, used)])
Proof step 361:
# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[vtblpnum1] = wl-entry(m0, used), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), aehdr.valid?, vtblpnum1 < # wlar, n1 < # wlar, bflipset-cons(bflipset -- vtblpnum1, wlar), bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, sqnum + 1), valid-peb(mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ LEB_SIZE ⊦ vtblpnum1 = n1, valid-wl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)]), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, n1 < # apebs0 ∧ # apebs0 = # wlar[vtblpnum1, wl-entry(m0, erasing)] ∧ valid-wl(apebs0, wlar[vtblpnum1, wl-entry(m0, erasing)]) ∧ valid-peb(mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)) ∧ ( valid-sqns (mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).vidhdr.vol, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).vidhdr.leb, apebs0) ≠ ∅ → mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).vidhdr.sqn > valid-sqns (mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).vidhdr.vol, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).vidhdr.leb, apebs0) .max) ∧ (∀ m. m < # wlar[vtblpnum1, wl-entry(m0, erasing)] ∧ m ≠ n1 ∧ wlar[vtblpnum1, wl-entry(m0, erasing)][m].status = used → apebs0[m].vidhdr.vol ≠ mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).vidhdr.vol ∨ apebs0[m].vidhdr.leb ≠ mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).vidhdr.leb) ∧ mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false).echdr.ec = m1

Rule argument

spec: ubi-base name: valid-wl-use seq: n < # apebs, # apebs = # wlar ⊦ valid-wl(apebs, wlar) ∧ valid-peb(apeb) ∧ ( valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs) ≠ ∅ → apeb.vidhdr.sqn > valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs) .max) ∧ (∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ apeb.vidhdr.vol ∨ apebs[m].vidhdr.leb ≠ apeb.vidhdr.leb) ∧ apeb.echdr.ec = m0 → valid-wl(apebs[n, apeb], wlar[n, wl-entry(m0, used)]) subst: [m0, wlar, apeb, n, apebs] → [m1, wlar[vtblpnum1, wl-entry(m0, erasing)], mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false), n1, apebs0] flags: <all paths>

Additional information

Used terms: m1, wlar[vtblpnum1, wl-entry(m0, erasing)], mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false), n1, apebs0