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Proof step 368 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, LEB_SIZE = n2 + n0, wlar[vtblpnum1, wl-entry(m0, erasing)][m] = wl-entry(m4, used), apebs0[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), wlar[vtblpnum1] = wl-entry(m0, used), apebs0[n1] = mkpeb(aechdr(m2), empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), m < # wlar, vtblpnum1 < # wlar, n1 < # wlar, valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs0).max < sqnum, 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(aechdr(m2), avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m3, boolvar)), 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(aechdr(m2), 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 ⊦ m = n1, vtblpnum1 = n1, valid-wl (apebs0[n1, mkpeb(aechdr(m2), 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: wlarray-base name: Put-other seq: ⊦ m ≠ n → wlar[n, wle][m] = wlar[m] subst: [m, wle, n, wlar] → [m, wl-entry(m0, erasing), vtblpnum1, wlar] flags: <all paths>

Additional information

Used simplifier rules: lf-valid-wl-not-erroneous: n < # wlar, stat ≠ erroneous ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ wlar[n] = wl-entry(m0, stat) ∧ valid-wl(apebs, wlar) → ¬ boolvar;%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;%is-vtbl-pnum: n < # apebs, n < # wlar ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ wlar[n] = wl-entry(m0, used) ∧ valid-wl(apebs, wlar) ∧ avhdr.vol = VTBL_VOLID ∧ avhdr.leb = VTBL_LNUM ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ ¬ VTBL_VOLID ∈ vols → n = n0; (forward) from specification ubi-base% ⊦ used ≠ erroneous; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ used ≠ erasing; (s) Used terms: m, wl-entry(m0, erasing), vtblpnum1, wlar