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Proof step 404 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[m] = wl-entry(m2, used), vols[v][m0] = ⌜m⌝ , wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, m0 < # vols[v], n1 < # wlar, m < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset -- m, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), 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(m, v × m0) '), valid-global-sqn(apebs0, sqnum + 1), valid-global-sqn(apebs0, sqnum), valid-peb(mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-peb(v, m0, apebs0[m]), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ LEB_SIZE ⊦ m = n1, m = vtblpnum1, vtblpnum1 = n1, valid-ebatbl (apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[n1, wl-entry(m1, used)][m, wl-entry(m2, erasing)], vols[v, vols[v][m0, ⌜n1⌝ ]], vtblpnum1), m ∈ q, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-ebatbl-remap seq: n < # wlar, n < # apebs ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n1⌝ ∧ n ≠ n0 ∧ n1 ≠ n0 ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ wlar[n].status ≠ used ∧ valid-ebatbl(apebs, wlar, vols, n0) → valid-ebatbl (apebs, wlar[n, wl-entry(m0, used)][n1, wl-entry(m1, erasing)], vols[v, vols[v][m, ⌜n⌝ ]], n0) subst: [n0, m, v, vols, m1, n1, m0, n, wlar, apebs] → [vtblpnum1, m0, v, vols, m2, m, m1, n1, wlar, apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false) ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # apebs[n, apeb] = # apebs; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ used ≠ free; (s)%stat ≠ used ⊦ wlar[m] = wl-entry(m0, stat) → ( valid-ebatbl(apebs[m, apeb], wlar, vols, n) ↔ valid-ebatbl(apebs, wlar, vols, n)); (ss) Used terms: vtblpnum1, m0, v, vols, m2, m, m1, n1, wlar, apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false) ]