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Proof step 79 from proof refine-write (previous step)

# apebs0 = # wlar, LEB_SIZE - vtblpnum5 = n0 + n, apebs0[n2] = mkpeb(aehdr, avhdr, buf2, m0, false), vols[v][vtblpnum3] = ⌜n2⌝ , avols[v][vtblpnum3] = mapped(buf2, m), wlar[n2] = wl-entry(m1, used), n ≠ 0, vtblpnum4 ≠ n2, aehdr.valid?, avhdr.valid?, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n2 < # wlar, abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0), unique-sqns(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)]), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-ebatbl (apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-wl(apebs0, wlar), valid-wl(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], wlar), v ∈ vols, v ∈ avols, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 + n ≤ LEB_SIZE, n + n3 ≤ # buf, m ≤ vtblpnum5, m0 ≤ vtblpnum5, vtblpnum5 ≤ LEB_SIZE, n + vtblpnum5 ≤ LEB_SIZE, n3 + n ≤ # buf, ¬ VTBL_VOLID ∈ vols ⊦ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n, buf; avols; err1)⟩ ( abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb (apebs0[vols[v][vtblpnum3].pnum].echdr, apebs0[vols[v][vtblpnum3].pnum].vidhdr, subarray(apebs0[vols[v][vtblpnum3].pnum].data, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, apebs0[vols[v][vtblpnum3].pnum].bad) ], vols, q) ∧ ESUCCESS = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 80:
# apebs0 = # wlar, LEB_SIZE = n1 + vtblpnum5, wlar[n2] = wl-entry(m1, used), avols[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n2⌝ , apebs0[n2] = mkpeb(aehdr, avhdr, buf2, m0, false), n1 = n0 + n, avhdr.valid?, aehdr.valid?, n2 < # wlar, vtblpnum3 < # avols[v], vtblpnum3 < # vols[v], abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)]), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)]), unique-sqns(apebs0), valid-ebatbl (apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], wlar, vols, vtblpnum4), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-eraseq(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], q), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-wl(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], wlar), valid-wl(apebs0, wlar), v ∈ avols, v ∈ vols, n3 + n ≤ # buf, n + vtblpnum5 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n + n3 ≤ # buf, vtblpnum5 + n ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n, buf; avols; err1)⟩ ( abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb (apebs0[vols[v][vtblpnum3].pnum].echdr, apebs0[vols[v][vtblpnum3].pnum].vidhdr, subarray(apebs0[vols[v][vtblpnum3].pnum].data, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, apebs0[vols[v][vtblpnum3].pnum].bad) ], vols, q) ∧ ESUCCESS = err1), n = 0, vtblpnum4 = n2, VTBL_VOLID ∈ vols

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE, vtblpnum5, n1]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, vtblpnum5, n1