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Proof step 148 from proof prepost-write-once (previous step)

# apebs0 = # wlar1, # apebs2 = # wlar0, q0.head = eq-entry(m4, lref0), LEB_SIZE = (n2 + m0) + m1, vols0[v][m] = unmapped, wlar0[vtblpnum1] = wl-entry(m5, free), apebs2[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, m < # vols0[v], vtblpnum1 < # wlar0, bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset, wlar0), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), ubi-io-inv(apebs2), unique-sqns(apebs0), unique-sqns(apebs2), valid-ebatbl(apebs0, wlar1, vols0, vtblpnum2), valid-ebatbl(apebs2, wlar0, vols0, vtblpnum2), valid-eraseq(q1 + eq-entry(vtblpnum1, v × m) '), valid-eraseq(apebs0, q0), valid-eraseq(wlar1, q0), valid-eraseq(q0), valid-eraseq(q1), valid-eraseq(wlar0, q1), valid-eraseq(apebs2, q1), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs2, sqnum), valid-peb(mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols0, wlar1, vtblpnum2), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-wl(apebs0, wlar1), valid-wl(apebs2, wlar0), v ∈ vols0, m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m0 + m1 ≤ LEB_SIZE, q1.lebrefs ⊆ q0.lebrefs, ⌊err0⌋ , apebs0 = apebs2 ∧ wlar1 = wlar0 ∧ q0 = q1 ∨ id○(apebs0, apebs2, vtblpnum1) ∧ id○(wlar1, wlar0, vtblpnum1) ∧ q0 = eq-entry(vtblpnum1, lref0) ' + q1 ⊦ m1 = 0, vtblpnum2 = vtblpnum1, valid-global-sqn(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], sqnum + 1), vtblpnum2 ∈ q1, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-global-sqn-add-valid seq: m < # apebs ⊦ valid-peb(apeb) ∧ valid-global-sqn(apebs, n) ∧ apeb.vidhdr.sqn < n → valid-global-sqn(apebs[m, apeb], n) subst: [n, apeb, m, apebs] → [sqnum + 1, mkpeb (aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false), vtblpnum1, apebs2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ valid-global-sqn(apebs, n) → valid-global-sqn(apebs, n + m); (ss)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (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 Used terms: sqnum + 1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false), vtblpnum1, apebs2