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Proof step 194 from proof refine-write (previous step)

⟨fail_or_success#(; ; err)⟩ (err = err1), # 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⌝ , avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(LEB_SIZE - n), n)]] = avols1, avols = avols0, avols0 = avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]], buf = subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n5), err1 = ESUCCESS, err1 = err2, n = vtblpnum5 + n5, vtblpnum = vtblpnum3, avhdr.valid?, aehdr.valid?, n4 < # wlar, vtblpnum3 < # avols2[v], vtblpnum3 < # vols[v], n2 < n5, vtblpnum < # avols[v], 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(avols1, 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(n, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(vtblpnum5, 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, v ∈ avols, n ≤ # buf, n ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, n2 + vtblpnum5 ≤ LEB_SIZE, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n5 + n3 ≤ # buf0, vtblpnum5 + n5 ≤ LEB_SIZE, n3 + n2 ≤ # buf0, 0 + vtblpnum5 ≤ # buf2, n3 + n5 ≤ # buf0, 0 + n ≤ # buf, LEB_SIZE ≥ n, ⌊err3⌋ , v ∈ avols → v ∈ avols ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; if err = ESUCCESS then if avols2[v][vtblpnum3].mapped? then if n5 ≠ 0 then avols2[v][vtblpnum3] := mapped (subarray(avols2[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n5) + mkempbuf(LEB_SIZE - vtblpnum5 - n5), vtblpnum5 + n5) else avols2[v][vtblpnum3] := mapped(mkempbuf(vtblpnum5) + subarray(buf0, n3, n5) + mkempbuf(LEB_SIZE - vtblpnum5 - n5), vtblpnum5 + n5) else if avols2[v][vtblpnum3].mapped? then choose n with n < n5 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avols2[v][vtblpnum3] := mapped (subarray(avols2[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n) + mkempbuf(LEB_SIZE - vtblpnum5 - n), vtblpnum5 + n) ifnone skip else if n5 ≠ 0 then avols2[v][vtblpnum3] := unmapped⟩ (abs(avols2, apebs1, vols0, q0) ∧ err2 = err), n2 = 0, vtblpnum4 = n4, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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)% ⊦ mapped(buf, m).mapped?; (s)% ⊦ m < # evol → evol[m, leb][m] = leb; (s)% ⊦ m < n → n ≠ 0; (s)%abs-vols-mapped: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ abs(avols, apebs, vols, q) → avols[v][m].mapped?; (forward) from specification ubi-abs%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ∈ avols[v0, evol] ↔ v = v0 ∨ v ∈ avols; (ws)% ⊦ m < n → m ≤ n; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ # evol[n, leb] = # evol; (s)% ⊦ avols[v, evol][v, evol0] = avols[v, evol0]; (s)%m < # evol ⊦ evol[m, leb][m, leb0] = evol[m, leb0]; (s)%⊦ v ∈ vols ∧ m < # vols[v] ∧ abs(avols, apebs, vols, q) → m < # avols[v]; (ss)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ avols[v, evol][v] = evol; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ v ∈ avols[v, evol]; (s)%⊦ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, n) ∧ ebm-cons(avols) → # buf = LEB_SIZE; (s)% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)