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Proof step 18 from proof inv-write (previous step)

# apebs = # wlar, vols[v][vtblpnum4] = ⌜m0⌝ , apebs[m0] = mkpeb(aehdr, avhdr, buf1, m, false), wlar[m0] = wl-entry(m1, used), m0 ≠ vtblpnum, n ≠ 0, vtblpnum4 < # vols[v], m0 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum3, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf1, m, false)), valid-peb(mkpeb(aehdr, avhdr, buf1, m, false)), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), v ∈ vols, n0 + n ≤ # buf, vtblpnum3 + n ≤ LEB_SIZE, m ≤ vtblpnum3, ¬ m0 ∈ q, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q ⊦ ⟪aubi_io_write_data#(m0, vtblpnum3, n0, n, buf; apebs; err); if err ≠ ESUCCESS then {debug#("ubi: failed to write to PEB " + m0.toString); let buf1 = mkbuf(vtblpnum3 + n), bitflips = ? in {aubi_io_read_data#(m0, 0, 0, vtblpnum3, apebs; buf1; bitflips, err); if err = ESUCCESS then {buf1 := copy(buf, n0, buf1, vtblpnum3, n); debug#("ubi: moving data from PEB " + m0.toString); ubi_change#(v, vtblpnum4, vtblpnum3 + n, buf1, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)} else debug#("ubi: failed to read data from PEB " + m0.toString)}}⟫ ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ 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, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs))

User applied rule insert program lemma

And obtained the following new goals

Proof step 19:
ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1), ubi-io-inv(apebs), n < # apebs, is-aligned(m0, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), apebs[n].fill ≤ m0, m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, wlar[n].status = used, n0 ≠ n ⊦ ⟪aubi_io_write_data#(n, m0, m1, m2, buf; apebs; err)⟫ (ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ∧ ubi-io-inv(apebs))
Proof step 20:
# apebs = # wlar, wlar[m0].status = used, wlar[m0] = wl-entry(m1, used), apebs[m0] = mkpeb(aehdr, avhdr, buf1, m, false), vols[v][vtblpnum4] = ⌜m0⌝ , bflipset0 = bflipset, buf0 = buf, m3 = vtblpnum3, m4 = n, m5 = n0, n2 = vtblpnum, n3 = sqnum, n4 = m0, q0 = q, vols0 = vols, wlar0 = wlar, m0 < # wlar, vtblpnum4 < # vols[v], m0 < # apebs, bflipset-cons(bflipset, wlar), is-aligned(vtblpnum3, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-peb(mkpeb(aehdr, avhdr, buf1, m, false)), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf1, m, false)), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), v ∈ vols, m ≤ vtblpnum3, apebs[m0].fill ≤ vtblpnum3, vtblpnum3 + n ≤ LEB_SIZE, n0 + n ≤ # buf ⊦ [aubi_io_write_data#(m0, vtblpnum3, n0, n, buf; apebs; err)] ( ubi-cons(apebs, vols0, wlar0, q0, bflipset0, n2, n3) ∧ ubi-io-inv(apebs) → ⟪if err ≠ ESUCCESS then {debug#("ubi: failed to write to PEB " + m0.toString); let buf1 = mkbuf(vtblpnum3 + n), bitflips = ? in {aubi_io_read_data#(m0, 0, 0, vtblpnum3, apebs; buf1; bitflips, err); if err = ESUCCESS then {buf1 := copy(buf, n0, buf1, vtblpnum3, n); debug#("ubi: moving data from PEB " + m0.toString); ubi_change#(v, vtblpnum4, vtblpnum3 + n, buf1, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)} else debug#("ubi: failed to read data from PEB " + m0.toString)}}⟫ ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ 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, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs))), m0 = vtblpnum, n = 0, m0 ∈ q, VTBL_VOLID ∈ vols, vtblpnum ∈ q

Rule argument

spec: <toplevel> name: prepost-io-write-data seq: ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1), ubi-io-inv(apebs), n < # apebs, is-aligned(m0, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), apebs[n].fill ≤ m0, m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, wlar[n].status = used, n0 ≠ n ⊦ ⟪aubi_io_write_data#(n, m0, m1, m2, buf; apebs; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ∧ ubi-io-inv(apebs)) subst: [buf, m2, m1, m0, n, apebs, err, vols, wlar, q, bflipset, n0, n1] → [buf, n, n0, vtblpnum3, m0, apebs, err, vols, wlar, q, bflipset, vtblpnum, sqnum] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ wl-entry(m, stat).status = stat; (s)