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Proof step 138 from proof refine-write (previous step)

# apebs0 = # wlar, LEB_SIZE = (n1 + n2) + vtblpnum5, apebs0[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), wlar[n4] = wl-entry(m1, used), avols[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n4⌝ , n2 ≠ 0, vtblpnum4 ≠ n4, avhdr.valid?, aehdr.valid?, n4 < # wlar, n2 < n5, vtblpnum3 < # avols[v], vtblpnum3 < # vols[v], abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]), unique-sqns(apebs0), valid-ebatbl (apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], wlar, vols, vtblpnum4), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-eraseq(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 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(buf, n3, n2) + mkempbuf(n1), 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(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], wlar), valid-wl(apebs0, wlar), v ∈ vols, v ∈ avols, n3 + n2 ≤ # buf, vtblpnum5 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, n2 + vtblpnum5 ≤ LEB_SIZE, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n5 + n3 ≤ # buf, n3 + n5 ≤ # buf, vtblpnum5 + n5 ≤ LEB_SIZE, ⌊err3⌋ , ¬ VTBL_VOLID ∈ vols ⊦ ⟪debug#("ubi: moving data from PEB " + vols[v][vtblpnum3].pnum.toString); apebs := apebs0[vols[v][vtblpnum3].pnum, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]; ubi_change# (v, vtblpnum3, vtblpnum5 + n5, copy(buf, n3, copy(subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 0, mkbuf(vtblpnum5 + n5), 0, vtblpnum5), vtblpnum5, n5), EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs ; err)⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n5, buf; avols; err1)⟩ (abs(avols, apebs, vols, q) ∧ err = err1)

User applied rule insert program lemma

And obtained the following new goals

Proof step 139:
⊦ ⟪debug#(str)⟫ true
Proof step 140:
# apebs0 = # wlar, LEB_SIZE = (n1 + 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), str0 = "ubi: moving data from PEB " + vols[v][vtblpnum3].pnum.toString, aehdr.valid?, avhdr.valid?, vtblpnum3 < # avols[v], n2 < n5, n4 < # wlar, vtblpnum3 < # vols[v], 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), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 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(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)]), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-ebatbl (apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 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(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 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(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false)], wlar), v ∈ avols, v ∈ vols, vtblpnum5 + n5 ≤ LEB_SIZE, n3 + n5 ≤ # buf, n5 + n3 ≤ # buf, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n2 + vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, n3 + n2 ≤ # buf, ⌊err3⌋ ⊦ ∀ . true → ⟪apebs := apebs0 [vols[v][vtblpnum3].pnum, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), vtblpnum5 + n2, false) ]; ubi_change# (v, vtblpnum3, vtblpnum5 + n5, copy (buf, n3, copy(subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n2) + mkempbuf(n1), 0, mkbuf(vtblpnum5 + n5), 0, vtblpnum5), vtblpnum5, n5), EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs ; err)⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n5, buf; avols; err1)⟩ (abs(avols, apebs, vols, q) ∧ err = err1), vols[v][vtblpnum3] = unmapped, n2 = 0, vtblpnum4 = n4, VTBL_VOLID ∈ vols

Rule argument

spec: debug name: debug seq: ⊦ ⟪debug#(str)⟫ true subst: [str] → [ "ubi: moving data from PEB " + vols[v][vtblpnum3].pnum.toString] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ∈ avols ∧ m < # avols[v] ∧ abs(avols, apebs, vols, q) → m < # vols[v]; (ss)% ⊦ v ∈ avols ∧ abs(avols, apebs, vols, q) → v ∈ vols; (ss)%abs-vols-unmapped: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = unmapped ∧ abs(avols, apebs, vols, q) → ¬ avols[v][m].mapped?; (forward) from specification ubi-abs% ⊦ unmapped ≠ ⌜m⌝ ; (s)