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Proof step 280 from proof refine-write (previous step)

# buf0 = vtblpnum5 + n5, # apebs0 = # wlar, LEB_SIZE = (n0 + n2) + vtblpnum5, LEB_SIZE = n6 + 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), n6 = n1 + n2, aehdr.valid?, avhdr.valid?, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n2 < n5, n4 < # wlar, n < n5, 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), is-aligned(n, EB_PAGE_SIZE), range=(buf0, vtblpnum5, mkbuf(vtblpnum5 + n5), vtblpnum5, n5), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), 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(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)]), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-ebatbl (apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), 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(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), 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(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], wlar), v ∈ vols, v ∈ avols, n2 + vtblpnum5 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 + n5 ≤ LEB_SIZE, n3 + n5 ≤ # buf3, n5 + n3 ≤ # buf3, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n3 + n2 ≤ # buf3, ⌊err1⌋ , ⌊err3⌋ ⊦ n2 = 0, vtblpnum4 = n4, abs (avols[v, avols[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2)]], apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], vols, q), VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 281:
# apebs0 = # wlar, # buf0 = vtblpnum5 + n5, LEB_SIZE = (n1 + n2) + vtblpnum5, apebs0[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), wlar[n4] = wl-entry(m1, used), avols[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n4⌝ , avhdr.valid?, aehdr.valid?, n < n5, n2 < n5, vtblpnum3 < # avols[v], vtblpnum3 < # vols[v], n4 < # wlar, abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), range=(buf0, vtblpnum5, mkbuf(vtblpnum5 + n5), vtblpnum5, n5), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]), unique-sqns(apebs0), valid-ebatbl (apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], wlar, vols, vtblpnum4), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-eraseq(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], q), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-wl(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], wlar), valid-wl(apebs0, wlar), v ∈ avols, v ∈ vols, n3 + n2 ≤ # buf3, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n5 + n3 ≤ # buf3, n3 + n5 ≤ # buf3, vtblpnum5 + n5 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, n2 + vtblpnum5 ≤ LEB_SIZE, ⌊err3⌋ , ⌊err1⌋ ⊦ n2 = 0, vtblpnum4 = n4, abs (avols[v, avols[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2)]], apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], vols, q), VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: lf-mapped-in-apebs: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → n < # apebs;% ⊦ # apebs[n, apeb] = # apebs; (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic