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Proof step 226 from proof refine-write (previous step)

# apebs0 = # wlar, LEB_SIZE = (n0 + n2) + vtblpnum5, apebs0[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), wlar[n4] = wl-entry(m1, used), avols2[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n4⌝ , n2 ≠ 0, vtblpnum4 ≠ n4, avhdr.valid?, aehdr.valid?, vtblpnum3 < # avols2[v], n4 < # wlar, vtblpnum3 < # vols[v], n2 < n5, n < n5, abs(avols2, apebs0, vols, q), abs (avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]], apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], vols, q), abs(avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]], apebs1, vols0, q0), bflipset-cons(bflipset, wlar), ebm-cons(avols2), ebm-cons(avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]]), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)]), unique-sqns(apebs0), valid-ebatbl (apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], wlar, vols, vtblpnum4), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-eraseq(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), 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(buf0, n3, n2) + mkempbuf(n0), 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(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], wlar), valid-wl(apebs0, wlar), v ∈ avols2, v ∈ vols, vtblpnum5 + n5 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, n2 + vtblpnum5 ≤ LEB_SIZE, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n5 + n3 ≤ # buf0, n3 + n2 ≤ # buf0, n3 + n5 ≤ # buf0, ⌊err2⌋ , ⌊err3⌋ , ¬ VTBL_VOLID ∈ vols ⊦ ∃ n1. n1 < n5 ∧ is-aligned(n1, EB_PAGE_SIZE) ∧ ⟨if n1 ≠ 0 then avols2[v][vtblpnum3] := mapped (subarray(avols2[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n1) + mkempbuf(LEB_SIZE - vtblpnum5 - n1), vtblpnum5 + n1)⟩ abs(avols2, apebs1, vols0, q0)

User applied rule exists right

And obtained the following new goals

Proof step 227:
# apebs0 = # wlar, LEB_SIZE = (n0 + n2) + vtblpnum5, vols[v][vtblpnum3] = ⌜n4⌝ , avols2[v][vtblpnum3] = mapped(buf2, m), wlar[n4] = wl-entry(m1, used), apebs0[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), aehdr.valid?, avhdr.valid?, n < n5, n2 < n5, vtblpnum3 < # vols[v], n4 < # wlar, vtblpnum3 < # avols2[v], abs(avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]], apebs1, vols0, q0), abs (avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]], apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], vols, q), abs(avols2, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]]), ebm-cons(avols2), is-aligned(n, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)]), ubi-io-inv(apebs0), 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(buf0, 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(buf0, 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(buf0, 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(buf0, 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(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], wlar), v ∈ vols, v ∈ avols2, n3 + n5 ≤ # buf0, n3 + n2 ≤ # buf0, n5 + n3 ≤ # buf0, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n2 + vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, vtblpnum5 + n5 ≤ LEB_SIZE, ⌊err3⌋ , ⌊err2⌋ ⊦ n2 < n5 ∧ is-aligned(n2, EB_PAGE_SIZE) ∧ ⟨if n2 ≠ 0 then avols2[v][vtblpnum3] := mapped(subarray(avols2[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(LEB_SIZE - vtblpnum5 - n2), vtblpnum5 + n2)⟩ abs(avols2, apebs1, vols0, q0), n2 = 0, vtblpnum4 = n4, VTBL_VOLID ∈ vols

Rule argument

pos: right 1 terms: n2 abort: F discard: T computed: T

Additional information

Used terms: n2