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Proof step 47 from proof inv-write (previous step)

# apebs1 = # wlar, # apebs0 = # wlar, apebs0[m0] = mkpeb(aehdr0, avhdr0, buf3, m2, false), vols[v][vtblpnum4] = ⌜m0⌝ , apebs1[m0] = mkpeb(aehdr, avhdr, buf2, m, false), wlar[m0] = wl-entry(m1, used), err1 ≠ ESUCCESS, m0 ≠ vtblpnum1, n2 ≠ 0, vtblpnum4 < # vols[v], m0 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n2, EB_PAGE_SIZE), is-aligned(vtblpnum3, EB_PAGE_SIZE), ubi-io-inv(apebs1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m, false)), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf3, m2, false)), unique-sqns(apebs1), unique-sqns(apebs0), valid-ebatbl(apebs1, wlar, vols, vtblpnum1), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs1, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs1, sqnum), valid-global-sqn(apebs0, sqnum), valid-peb(v, vtblpnum4, mkpeb(aehdr0, avhdr0, buf3, m2, false)), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(mkpeb(aehdr0, avhdr0, buf3, m2, false)), valid-vtbl(apebs1, vols, wlar, vtblpnum1), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs1, wlar), valid-wl(apebs0, wlar), v ∈ vols, m ≤ vtblpnum3, n1 + n2 ≤ # buf, vtblpnum3 + n2 ≤ LEB_SIZE, m ≤ LEB_SIZE, vtblpnum3 ≤ LEB_SIZE, ¬ vtblpnum1 ∈ q, ¬ m0 ∈ q, ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_change# (v, vtblpnum4, vtblpnum3 + n2, copy(buf, n1, copy(buf3, 0, mkbuf(vtblpnum3 + n2), 0, vtblpnum3), vtblpnum3, n2), EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum1, sqnum, apebs0 ; err)⟫ ( # apebs0 = # wlar ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs0, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs0, wlar, vols, vtblpnum1) ∧ valid-vtbl(apebs0, vols, wlar, vtblpnum1) ∧ ubi-io-inv(apebs0))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: inv-change seq: ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), vtblpnum0 = EB_PAGE_SIZE, ubi-io-inv(apebs), n0 ≤ LEB_SIZE, n0 ≤ # buf, v ∈ vols, vtblpnum1 < # vols[v], is-aligned(n0, EB_PAGE_SIZE), vols0 = vols, apebs0 = apebs, q0 = q ⊦ ⟪ubi_change# (v, vtblpnum1, n0, buf, vtblpnum0 ; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs ; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err ≠ ESUCCESS → vols = vols0 ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q0.lebrefs) ∧ ( err = ESUCCESS → v ∈ vols0 ∧ vtblpnum1 < # vols0[v] ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × vtblpnum1) ∧ ( vols0[v][vtblpnum1] ≠ unmapped → id (apebs, apebs0, mapped-pebs(vols0) -- vols0[v][vtblpnum1].pnum)) ∧ ( vols0[v][vtblpnum1] = unmapped → id(apebs, apebs0, mapped-pebs(vols0))) ∧ (∃ n. vols = vols0[v, vols0[v][vtblpnum1, ⌜n⌝ ]] ∧ apebs[n].data = subarray(buf, 0, n0) + mkempbuf(LEB_SIZE - n0) ∧ apebs[n].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE)))) subst: [vtblpnum0, buf, n0, vtblpnum1, v, apebs, sqnum, vtblpnum, bflipset, q, wlar, vols, err, vols0, apebs0, q0] → [EB_PAGE_SIZE, copy (buf, n1, copy(buf3, 0, mkbuf(vtblpnum3 + n2), 0, vtblpnum3), vtblpnum3, n2), vtblpnum3 + n2, vtblpnum4, v, apebs0, sqnum, vtblpnum1, bflipset, q, wlar, vols, err, vols, apebs0, q] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ↔ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)