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Proof step 40 from proof refine-write (previous step)

# apebs0 = # wlar0, # apebs = # wlar, LEB_SIZE = (n0 + n) + vtblpnum5, apebs0[n3] = mkpeb(aehdr, avhdr, mkempbuf(vtblpnum5) + subarray(buf, n4, n) + mkempbuf(n0), m, boolvar), vols[v][vtblpnum3] = unmapped, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], abs(avols, apebs, vols, q), abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols)), is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols[v, vols[v][vtblpnum3, ⌜n3⌝ ]], vtblpnum4), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols, wlar0, vtblpnum4), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, n + vtblpnum5 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, n ≤ LEB_SIZE, n + n4 ≤ # buf, n4 + n ≤ # buf, vtblpnum5 + n ≤ LEB_SIZE, q0.lebrefs ⊆ q.lebrefs ++ (v × vtblpnum3), n = 0 → q0.lebrefs ⊆ q.lebrefs, n ≠ 0 → m = vtblpnum5 + n, n = 0 → m = 0 ⊦ avols[v][vtblpnum3].mapped?, abs (avols[v, avols[v][vtblpnum3, mapped(mkempbuf(vtblpnum5) + subarray(buf, n4, n) + mkempbuf(n0), vtblpnum5 + n)]], apebs0, vols[v, vols[v][vtblpnum3, ⌜n3⌝ ]], q0), abs (avols[v, avols[v][vtblpnum3, mapped(mkempbuf(vtblpnum5) + subarray(buf, n4, n) + mkempbuf(n0), vtblpnum5 + n)]], apebs0, vols[v, vols[v][vtblpnum3, ⌜n3⌝ ]], q), VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-abs name: absexpt-mapped-abs seq: ⊦ abs○(avols, apebs, vols, q, v, m) ∧ v ∈ vols ∧ m < # vols[v] ∧ avols[v][m] = mapped(buf, m0) ∧ vols[v][m] = ⌜n⌝ ∧ apebs[n].data = buf ∧ apebs[n].fill ≤ m0 → abs(avols, apebs, vols, q) subst: [v, m, buf, m0, n, q, vols, apebs, avols] → [v, vtblpnum3, mkempbuf(vtblpnum5) + subarray(buf, n4, n) + mkempbuf(n0), vtblpnum5 + n, n3, q, vols[v, vols[v][vtblpnum3, ⌜n3⌝ ]], apebs0, avols [v, avols[v] [vtblpnum3, mapped (mkempbuf(vtblpnum5) + subarray(buf, n4, n) + mkempbuf(n0), vtblpnum5 + n) ] ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ∈ vols[v, ebatbl]; (s)% ⊦ vols[v, ebatbl][v] = ebatbl; (s)% ⊦ # ebatbl[n, ebae] = # ebatbl; (s)%⊦ v ∈ avols ∧ m < # avols[v] ∧ abs(avols, apebs, vols, q) → m < # vols[v]; (ss)% ⊦ avols[v, evol][v] = evol; (s)% ⊦ m < # evol → evol[m, leb][m] = leb; (s)% ⊦ m < # ebatbl → ebatbl[m, ebae][m] = ebae; (s)% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)%⊦ v ∈ avols ∧ m < # avols[v] → ( abs○(avols[v, avols[v][m, leb]], apebs, vols, q, v, m) ↔ abs○(avols, apebs, vols, q, v, m)); (ss)%⊦ v ∈ vols ∧ m < # vols[v] → ( abs○(avols, apebs, vols[v, vols[v][m, ebae]], q, v, m) ↔ abs○(avols, apebs, vols, q, v, m)); (ss)% ⊦ abs(avols, apebs, vols, q) → abs○(avols, apebs, vols, q, v, m); (ss)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: v, vtblpnum3, mkempbuf(vtblpnum5) + subarray(buf, n4, n) + mkempbuf(n0), vtblpnum5 + n, n3, q, vols[v, vols[v][vtblpnum3, ⌜n3⌝ ]], apebs0, avols [v, avols[v] [vtblpnum3, mapped (mkempbuf(vtblpnum5) + subarray(buf, n4, n) + mkempbuf(n0), vtblpnum5 + n) ] ]