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Proof step 77 from proof delta-atomic-leb-change (previous step)

vols[v][m2] = ⌜m⌝ , apebs0[n2] = mkpeb(aehdr, empty, buf1, 0, false), wlar[n2] = wl-entry(m0, stat), wlar[n1] = wl-entry(m1, stat0), align↑(datasize(buf, n0), EB_PAGE_SIZE) = align↑(datasize(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE)), EB_PAGE_SIZE), aehdr.valid?, m2 < # vols[v], n2 < # apebs0, n1 < # wlar, m < # wlar, n2 < # wlar, v ∈ vols, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, m = n1 ∨ v = VTBL_VOLID ∧ m2 = VTBL_LNUM ∧ vtblpnum1 = n1 ⊦ datasize(buf, n0) = 0, datasize(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE)) = 0, n2 = n1, v = VTBL_VOLID ∧ m2 = VTBL_LNUM, sum-of-differences (ecs(wlar[m, wl-entry(wlar[m].ec, erasing)][n2, wl-entry(wlar[m, wl-entry(wlar[m].ec, erasing)][n2].ec, used)]).max, ecs(wlar[m, wl-entry(wlar[m].ec, erasing)][n2, wl-entry(wlar[m, wl-entry(wlar[m].ec, erasing)][n2].ec, used)])) = sum-of-differences(ecs(wlar).max, ecs(wlar)) ∧ ecs(wlar[m, wl-entry(wlar[m].ec, erasing)][n2, wl-entry(wlar[m, wl-entry(wlar[m].ec, erasing)][n2].ec, used)]) = ecs(wlar) ∧ wlar[m, wl-entry(wlar[m].ec, erasing)][n2].ec = m0 ∧ wlar[m, wl-entry(wlar[m].ec, erasing)][n1].ec = m1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 78:
wlar[n1] = wl-entry(m1, stat0), wlar[n2] = wl-entry(m0, stat), apebs0[n2] = mkpeb(aehdr, empty, buf1, 0, false), vols[v][m2] = ⌜m⌝ , wlar[m, wl-entry(wlar[m].ec, erasing)][n2] = wl-entry(m3, stat1), align↑(datasize(buf, n0), EB_PAGE_SIZE) = align↑(datasize(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE)), EB_PAGE_SIZE), aehdr.valid?, n2 < # wlar, m < # wlar, n1 < # wlar, n2 < # apebs0, m2 < # vols[v], v ∈ vols, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, m = n1 ∨ v = VTBL_VOLID ∧ m2 = VTBL_LNUM ∧ vtblpnum1 = n1 ⊦ datasize(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE)) = 0, datasize(buf, n0) = 0, n2 = n1, sum-of-differences (ecs(wlar[m, wl-entry(wlar[m].ec, erasing)][n2, wl-entry(m3, used)]).max, ecs(wlar[m, wl-entry(wlar[m].ec, erasing)][n2, wl-entry(m3, used)])) = sum-of-differences(ecs(wlar).max, ecs(wlar)) ∧ ecs(wlar[m, wl-entry(wlar[m].ec, erasing)][n2, wl-entry(m3, used)]) = ecs(wlar) ∧ m3 = m0 ∧ wlar[m, wl-entry(wlar[m].ec, erasing)][n1].ec = m1, v = VTBL_VOLID ∧ m2 = VTBL_LNUM

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[m, wl-entry(wlar[m].ec, erasing)][n2], m3, stat1]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[m, wl-entry(wlar[m].ec, erasing)][n2], m3, stat1