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Proof step 348 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, 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(LEB_SIZE, EB_PAGE_SIZE), is-encoded(to-vtbl(vols), mkempbuf(LEB_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) ⊦ vtblpnum1 = n1, valid-vtbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], vols, wlar[n1, wl-entry(m1, used)], n1), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-vtbl seq: ⊦ valid-vtbl(apebs, vols, wlar, n0) ↔ n0 < # apebs ∧ n0 < # wlar ∧ wlar[n0].status = used ∧ apebs[n0].vidhdr.vol = VTBL_VOLID ∧ apebs[n0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[n0].data) subst: [n0, wlar, vols, apebs] → [n1, wlar[n1, wl-entry(m1, used)], vols, apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false) ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # apebs[n, apeb] = # apebs; (s)% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ is-encoded(vtbl0, buf) → (is-encoded(vtbl1, buf) ↔ vtbl0 = vtbl1); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s) Used terms: n1, wlar[n1, wl-entry(m1, used)], vols, apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false) ]