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Proof step 401 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 = vtblpnum1, vtblpnum1 = n1, valid-ebatbl (apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[m, wl-entry(m2, erasing)][n1, wl-entry(m1, used)], 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

Proof step 402:
m ≠ n ⊦ wlar[m, wle][n, wle0] = wlar[n, wle0][m, wle]
Proof step 403:
# apebs0 = # wlar, LEB_SIZE = n2 + n0, apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), vols[v][m0] = ⌜m⌝ , wlar[m] = wl-entry(m2, used), aehdr.valid?, m < # wlar, n1 < # wlar, m0 < # vols[v], bflipset-cons(bflipset -- m, wlar), bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q + eq-entry(m, v × m0) '), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, sqnum + 1), valid-peb(v, m0, apebs0[m]), valid-peb(mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ LEB_SIZE ⊦ m = vtblpnum1, m = n1, 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), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, m ∈ q

Rule argument

spec: array, inst: wlarray-base name: cputput-reverse seq: m ≠ n ⊦ wlar[m, wle][n, wle0] = wlar[n, wle0][m, wle] subst: [wle0, n, wle, m, wlar] → [wl-entry(m1, used), n1, wl-entry(m2, erasing), m, wlar] flags: <all paths>

Additional information

Used simplifier rules: lf-used-valid-peb: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ apebs[n] = apeb ∧ valid-wl(apebs, wlar) → valid-peb(apeb);%lf-used-info: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;%lf-mapped-valid-peb: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-wl(apebs, wlar) → valid-peb(v, m, apebs[n]);%lf-mapped-info: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → wlar[n].status = used ∧ n ≠ n0 ∧ n < # wlar;% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # wlar ⊦ valid-eraseq(wlar, q) ∧ wlar[n] = wl-entry(m, free) → ¬ n ∈ q; (s)%m < # wlar ⊦ wlar[m, wle][m, wle0] = wlar[m, wle0]; (s)% ⊦ ebatbl[n] = ebae → ebatbl[n, ebae] = ebatbl; (s)% ⊦ v ∈ vols → vols[v, vols[v]] = vols; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ used ≠ free; (s) Used terms: wl-entry(m1, used), n1, wl-entry(m2, erasing), m, wlar