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Proof step 58 from proof inv-wl-worker (previous step)

# apebs = # wlar, wlar[vtblpnum1] = wl-entry(m0, free), wlar[vtblpnum2] = wl-entry(m1, used), apebs[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs[vtblpnum2] = mkpeb(aehdr1, avhdr, buf, m3, false), apebs0 = apebs, q0 = q, vols0 = vols, vtblpnum4 ≠ vtblpnum1, aehdr.valid?, vtblpnum1 < # wlar, vtblpnum2 < # wlar, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr1, avhdr, buf, m3, 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-peb(mkpeb(aehdr1, avhdr, buf, m3, false)), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum4 ∈ q, ¬ vtblpnum2 ∈ q, bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0 ⊦ ⟪ubi_atomic_leb_change# (avhdr.vol, avhdr.leb, vtblpnum1, LEB_SIZE, copy(buf, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), EB_PAGE_SIZE ; vols, wlar, q, bflipset0, vtblpnum4, sqnum, apebs ; err0); if err0 ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum2.toString + " to PEB " + vtblpnum1.toString + " failed"); if err0 = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum2; wlar, apebs; err0); if err0 = ESUCCESS then q := q.butlast}⟫ ( # 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(bflipset0, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum4) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum4) ∧ ubi-io-inv(apebs) ∧ ( vols0 = vols ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols0 ∧ m < # vols0[v] ∧ vols0[v][m] ≠ unmapped ∧ vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs0, mapped-pebs(vols0) -- vols0[v][m].pnum) ∧ apebs[n].data = apebs0[vols0[v][m].pnum].data ∧ apebs[n].fill ≤ apebs0[vols0[v][m].pnum].fill ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m))))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: prepost-atomic-leb-change seq: ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), ubi-io-inv(apebs), n0 ≤ # buf, n < # wlar, n0 ≤ LEB_SIZE, wlar[n].status = free, apebs0 = apebs, is-aligned(n0, EB_PAGE_SIZE), v ∈ vols ∧ m < # vols[v] ∨ v = VTBL_VOLID ∧ m = VTBL_LNUM, vols0 = vols, q0 = q, vtblpnum0 = vtblpnum ⊦ ⟪ubi_atomic_leb_change# (v, m, n, n0, buf, EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs ; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(apebs, apebs0, n) ∧ ubi-io-inv(apebs) ∧ # 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) ∧ ( v ∈ vols0 ∨ is-encoded(to-vtbl(vols0), subarray(buf, 0, n0)) ∧ n0 = LEB_SIZE ∨ err ≠ ESUCCESS → valid-ebatbl(apebs, wlar, vols, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum)) ∧ ( err = ESUCCESS ∧ v = VTBL_VOLID ∧ m = VTBL_LNUM → (∀ v0, m0. ¬ v0 ∈ vols0 ∧ is-encoded (to-vtbl(vols0)[v0, m0], subarray(buf, 0, n0)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs, wlar, vols[v0, fill(mkebatbl(m0), unmapped)], vtblpnum) ∧ valid-vtbl (apebs, vols[v0, fill(mkebatbl(m0), unmapped)], wlar, vtblpnum))) ∧ ( err = ESUCCESS ∧ v ∈ vols0 ∧ vols0[v][m] ≠ unmapped → q = q0 + eq-entry(vols0[v][m].pnum, v × m)) ∧ ( err = ESUCCESS ∧ v = VTBL_VOLID ∧ m = VTBL_LNUM → q = q0 + eq-entry(vtblpnum0, v × m)) ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ ( v = VTBL_VOLID ∧ m = VTBL_LNUM ∨ err ≠ ESUCCESS → vols = vols0) ∧ ( v ∈ vols0 ∧ err = ESUCCESS → vols = vols0[v, vols0[v][m, ⌜n⌝ ]]) ∧ ( err = ESUCCESS → apebs[n].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE) ∧ apebs[n].data = subarray(buf, 0, n0) + mkempbuf(LEB_SIZE - n0) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m)) ∧ (err ≠ ESUCCESS → q.lebrefs = q0.lebrefs)) subst: [buf, n0, n, m, v, apebs, sqnum, vtblpnum, bflipset, q, wlar, vols, err, apebs0, vols0, q0, vtblpnum0] → [copy(buf, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), LEB_SIZE, vtblpnum1, avhdr.leb, avhdr.vol, apebs, sqnum, vtblpnum4, bflipset0, q, wlar, vols, err0, apebs, vols, q, vtblpnum4] flags: <all paths>

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