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Proof step 163 from proof refine-write (previous step)

# apebs0 = # wlar, LEB_SIZE = (n1 + n2) + vtblpnum5, vols[v][vtblpnum3] = ⌜n4⌝ , avols[v][vtblpnum3] = mapped(buf2, m), wlar[n4] = wl-entry(m1, used), apebs0[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), apebs = apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], n2 ≠ 0, vtblpnum4 ≠ n4, aehdr.valid?, avhdr.valid?, n4 < # wlar, vtblpnum3 < # avols[v], n2 < n5, vtblpnum3 < # vols[v], abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0), unique-sqns(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-ebatbl (apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-wl(apebs0, wlar), valid-wl(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], wlar), v ∈ vols, v ∈ avols, n3 + n2 ≤ # buf, vtblpnum5 + n5 ≤ LEB_SIZE, n5 + n3 ≤ # buf, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n2 + vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, n3 + n5 ≤ # buf, vtblpnum5 ≤ LEB_SIZE, ⌊err3⌋ , ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_change# (v, vtblpnum3, vtblpnum5 + n5, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n5), EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs ; err)⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n5, buf; avols; err1)⟩ (abs(avols, apebs, vols, q) ∧ err = err1)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: refine-change seq: v ∈ avols, vtblpnum < # avols[v], n ≤ LEB_SIZE, n ≤ # buf, is-aligned(n, EB_PAGE_SIZE), abs(avols, apebs, vols, q), ebm-cons(avols), ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum0, sqnum), vtblpnum1 = LEB_SIZE, vtblpnum2 = EB_PAGE_SIZE, ubi-io-inv(apebs) ⊦ ⟪ubi_change# (v, vtblpnum, n, buf, vtblpnum2 ; vols, wlar, q, bflipset, vtblpnum0, sqnum, apebs ; err)⟫ ⟨ebm_change#(v, vtblpnum, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0) subst: [vtblpnum2, buf, n, vtblpnum, v, apebs, sqnum, vtblpnum0, bflipset, q, wlar, vols, err, avols, vtblpnum1] → [EB_PAGE_SIZE, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n5), vtblpnum5 + n5, vtblpnum3, v, apebs, sqnum, vtblpnum4, bflipset, q, wlar, vols, err, avols [v, avols[v] [vtblpnum3, mapped ( subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2) ] ], LEB_SIZE] flags: <all paths>

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