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Proof step 270 from proof refine-write (previous step)

# buf0 = vtblpnum5 + n5, # apebs0 = # wlar, LEB_SIZE = (n0 + 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), buf = buf3, err = err1, n1 = n3, vtblpnum = vtblpnum5, vtblpnum0 = vtblpnum3, aehdr.valid?, avhdr.valid?, n4 < # wlar, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n2 < 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), 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, vtblpnum5 + n5 ≤ LEB_SIZE, n3 + n5 ≤ # buf3, n5 + n3 ≤ # buf3, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n2 + vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, n3 + n2 ≤ # buf3, ⌊err1⌋ , ⌊err3⌋ ⊦ (∀ n. ¬(n < n5 ∧ is-aligned(n, EB_PAGE_SIZE))) ∧ ⟨skip⟩ ( abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false) ], vols, q) ∧ err1 = err), ∃ n. (n < n5 ∧ is-aligned(n, EB_PAGE_SIZE)) ∧ ⟨if n ≠ 0 then avols[v][vtblpnum0] := mapped(subarray(avols[v][vtblpnum0].data, 0, vtblpnum) + subarray(buf, n1, n) + mkempbuf(LEB_SIZE - vtblpnum - n), vtblpnum + n)⟩ ( abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false) ], vols, q) ∧ err1 = err), n2 = 0, vtblpnum4 = n4, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 271:
# buf0 = vtblpnum5 + n5, # apebs0 = # wlar, LEB_SIZE = (n0 + 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), n2 ≠ 0, vtblpnum4 ≠ n4, aehdr.valid?, avhdr.valid?, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n2 < n5, n4 < # wlar, 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), 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, vtblpnum5 + n5 ≤ LEB_SIZE, n3 + n5 ≤ # buf3, n5 + n3 ≤ # buf3, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n2 + vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, n3 + n2 ≤ # buf3, ⌊err1⌋ , ⌊err3⌋ , ¬ VTBL_VOLID ∈ vols ⊦ ∃ n1. n1 < n5 ∧ is-aligned(n1, EB_PAGE_SIZE) ∧ ⟨if n1 ≠ 0 then avols[v][vtblpnum3] := mapped(subarray(avols[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf3, n3, n1) + mkempbuf(LEB_SIZE - vtblpnum5 - n1), vtblpnum5 + n1)⟩ abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false) ], vols, q), (¬ n < n5 ∨ ¬ is-aligned(n, EB_PAGE_SIZE)) ∧ ⟨skip⟩ abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf3, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false) ], vols, q)

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)