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Proof step 30 from proof prepost-write-multiple (previous step)

# apebs = # wlar, # apebs0 = # wlar0, # apebs2 = # wlar1, LEB_SIZE = (n1 + m0) + m1, vols0[v][m] = unmapped, apebs2[n] = mkpeb(aehdr, avhdr, buf0, m3, boolvar), m < # vols0[v], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar1), id(apebs, apebs0, mapped-pebs(vols0)), id(apebs2, apebs, mapped-pebs(vols0)), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-inv(apebs2), unique-sqns(apebs), unique-sqns(apebs0), unique-sqns(apebs2), valid-ebatbl(apebs, wlar, vols0, vtblpnum3), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-ebatbl(apebs2, wlar1, vols1, vtblpnum3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(apebs2, q2), valid-eraseq(wlar1, q2), valid-eraseq(q2), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs2, sqnum1), valid-vtbl(apebs, vols0, wlar, vtblpnum3), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-vtbl(apebs2, vols1, wlar1, vtblpnum3), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0), valid-wl(apebs2, wlar1), v ∈ vols0, m1 ≤ LEB_SIZE, m2 + m1 ≤ # buf, vtblpnum4 ≤ UBI_WRITE_RETRIES, m1 + m2 ≤ # buf, m0 + m1 ≤ LEB_SIZE, q2.lebrefs ⊆ q0.lebrefs ++ (v × m), q.lebrefs ⊆ q0.lebrefs ++ (v × m), q2.lebrefs ⊆ q.lebrefs ++ (v × m), ⌊err⌋ , err0 = ESUCCESS → vols1 = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → m3 = m0 + m1) ∧ (m1 = 0 → m3 = 0) ∧ buf0 = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n1), m1 = 0 → q.lebrefs ⊆ q0.lebrefs, err0 ≠ ESUCCESS → vols1 = vols0, m1 = 0 → q2.lebrefs ⊆ q.lebrefs, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ VTBL_VOLID ∈ vols0, vtblpnum3 ∈ q0, vtblpnum3 ∈ q, VTBL_VOLID ∈ vols1, vtblpnum3 ∈ q2, ( err0 = ESUCCESS → (∃ n. vols1 = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → apebs2[n].fill = m0 + m1) ∧ (m1 = 0 → apebs2[n].fill = 0) ∧ apebs2[n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n1))) ∧ (m1 = 0 → q2.lebrefs ⊆ q0.lebrefs) ∧ m < # vols1[v] ∧ v ∈ vols1

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 6

Additional information

Used simplifier rules: ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;%ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;% ⊦ # subarray(buf, m, n) = n; (s)%⊦ v ∈ vols → ( valid-vtbl(apebs, vols[v, vols[v][m, ebae]], wlar, n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)% ⊦ mkempbuf(n0) + mkempbuf(n1) = mkempbuf(n0 + n1); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ vols[v, ebatbl][v] = ebatbl; (s)% ⊦ # ebatbl[n, ebae] = # ebatbl; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 0 ≤ m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ s1 ⊆ s2 → s1 ⊆ s2 ++ lref; (s)%sub-ntrans: ⊦ s2 ⊆ s3 ∧ ¬ s2 ⊆ s4 → ¬ s3 ⊆ s4; (forward) from specification set-basic[lebrefset]%sub-trans: ⊦ s2 ⊆ s3 ∧ s3 ⊆ s4 → s2 ⊆ s4; (forward) from specification set-basic[lebrefset]%sub-ntrans-01: ⊦ s2 ⊆ s3 ∧ ¬ s4 ⊆ s3 → ¬ s4 ⊆ s2; (forward) from specification set-basic[lebrefset]