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Proof step 148 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 ≤ LEB_SIZE, vtblpnum5 + n5 ≤ LEB_SIZE, n5 + n3 ≤ # buf, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n2 + vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, n3 + n5 ≤ # buf, ⌊err3⌋ , ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_change# (v, vtblpnum3, vtblpnum5 + n5, subarray(copy(subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 0, mkbuf(vtblpnum5 + n5), 0, vtblpnum5), 0, vtblpnum5) + subarray(buf, n3, n5) + subarray(copy(subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 0, mkbuf(vtblpnum5 + n5), 0, vtblpnum5), vtblpnum5 + n5, 0), 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 rewrite lemma

And obtained the following new goals

Rule argument

spec: array-copy, inst: buffer name: subarray-copy-lower seq: n1 + n2 ≤ m0, m0 + m1 ≤ # buf ⊦ subarray(copy(buf0, n0, buf, n1, n2), m0, m1) = subarray(buf, m0, m1) subst: [m1, m0, n2, n1, buf, n0, buf0] → [0, vtblpnum5 + n5, vtblpnum5, 0, mkbuf(vtblpnum5 + n5), 0, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)%⊦ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, n) ∧ ebm-cons(avols) → # buf = LEB_SIZE; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: 0, vtblpnum5 + n5, vtblpnum5, 0, mkbuf(vtblpnum5 + n5), 0, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1)