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Proof step 64 from proof refine-write (previous step)

# apebs = # wlar, wlar[n1].status = used, avols[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n1⌝ , apebs[n1] = mkpeb(aehdr, avhdr, buf2, m0, false), n ≠ 0, vtblpnum4 ≠ n1, avhdr.valid?, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n1 < # wlar, abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, m ≤ vtblpnum5, n + n0 ≤ # buf, n0 + n ≤ # buf, vtblpnum5 + n ≤ LEB_SIZE, m0 ≤ vtblpnum5, ¬ VTBL_VOLID ∈ vols ⊦ [aubi_io_write_data#(vols[v][vtblpnum3].pnum, vtblpnum5, n0, n, buf; apebs; err)] ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(apebs, q) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum4) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum4) ∧ ubi-io-inv(apebs) → ⟪if err ≠ ESUCCESS then {debug#("ubi: failed to write to PEB " + vols[v][vtblpnum3].pnum.toString); let buf1 = mkbuf(vtblpnum5 + n), bitflips = ? in {aubi_io_read_data#(vols[v][vtblpnum3].pnum, 0, 0, vtblpnum5, apebs; buf1; bitflips, err); if err = ESUCCESS then {buf1 := copy(buf, n0, buf1, vtblpnum5, n); debug#("ubi: moving data from PEB " + vols[v][vtblpnum3].pnum.toString); ubi_change#(v, vtblpnum3, vtblpnum5 + n, buf1, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs; err)} else debug#("ubi: failed to read data from PEB " + vols[v][vtblpnum3].pnum.toString)}}⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n0, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 65:
# apebs = # wlar, apebs[n1] = mkpeb(aehdr, avhdr, buf2, m0, false), vols[v][vtblpnum3] = ⌜n1⌝ , avols[v][vtblpnum3] = mapped(buf2, m), wlar[n1] = wl-entry(m1, stat), stat = used, avhdr.valid?, n1 < # wlar, vtblpnum3 < # avols[v], vtblpnum3 < # vols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, m0 ≤ vtblpnum5, vtblpnum5 + n ≤ LEB_SIZE, n0 + n ≤ # buf, n + n0 ≤ # buf, m ≤ vtblpnum5 ⊦ [aubi_io_write_data#(vols[v][vtblpnum3].pnum, vtblpnum5, n0, n, buf; apebs; err)] ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(apebs, q) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum4) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum4) ∧ ubi-io-inv(apebs) → ⟪if err ≠ ESUCCESS then {debug#("ubi: failed to write to PEB " + vols[v][vtblpnum3].pnum.toString); let buf1 = mkbuf(vtblpnum5 + n), bitflips = ? in {aubi_io_read_data#(vols[v][vtblpnum3].pnum, 0, 0, vtblpnum5, apebs; buf1; bitflips, err); if err = ESUCCESS then {buf1 := copy(buf, n0, buf1, vtblpnum5, n); debug#("ubi: moving data from PEB " + vols[v][vtblpnum3].pnum.toString); ubi_change#(v, vtblpnum3, vtblpnum5 + n, buf1, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs; err)} else debug#("ubi: failed to read data from PEB " + vols[v][vtblpnum3].pnum.toString)}}⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n0, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0)), n = 0, vtblpnum4 = n1, VTBL_VOLID ∈ vols

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[n1], m1, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n1], m1, stat