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Proof step 95 from proof inv-wl-worker (previous step)

# apebs1 = # wlar, # apebs = # wlar, # wlar0 = # wlar, avhdr.sqn = valid-sqns(v, m, apebs).max, apebs[vtblpnum2] = mkpeb(aechdr(m1), avhdr, buf, m3, false), apebs[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[vtblpnum2] = wl-entry(m1, used), wlar[vtblpnum1] = wl-entry(m0, free), apebs1[vtblpnum1] = mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), vtblpnum4 ≠ vtblpnum1, aehdr.valid?, vtblpnum2 < # wlar, vtblpnum1 < # wlar, m < # vols[v], bflipset-cons(bflipset1, wlar0), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar), id(apebs1, apebs, mapped-pebs(vols)), id○(apebs1, apebs, vtblpnum1), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs1), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), ubi-io-peb-inv(mkpeb(aechdr(m1), avhdr, buf, m3, false)), unique-sqns(apebs1), unique-sqns(apebs), valid-ebatbl(apebs1, wlar0, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], vtblpnum), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q1), valid-eraseq(wlar0, q1), valid-eraseq(apebs1, q1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs1, sqnum0), valid-global-sqn(apebs, sqnum), valid-peb(v, m, mkpeb(aechdr(m1), avhdr, buf, m3, false)), valid-peb(mkpeb(aechdr(m1), avhdr, buf, m3, false)), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-wl(apebs1, wlar0), valid-wl(apebs, wlar), v ∈ vols, q1.lebrefs ⊆ q.lebrefs ++ (v × m), ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum4 ∈ q, ¬ vtblpnum2 ∈ q, ¬ vtblpnum ∈ q1, vols[v][m] ≠ unmapped → q1 = q + eq-entry(vols[v][m].pnum, v × m) ', bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0 ⊦ ⟪ubi_erase_worker_helper#(vtblpnum2; wlar0, apebs1; err); if err = ESUCCESS then q1 := q1.butlast⟫ ( # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum0) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0, q1) ∧ valid-eraseq(apebs1, q1) ∧ bflipset-cons(bflipset1, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], vtblpnum) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum) ∧ ubi-io-inv(apebs1) ∧ ( vols = vols[v, vols[v][m, ⌜vtblpnum1⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols[v, vols[v][m, ⌜vtblpnum1⌝ ]])) ∧ q1.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v0, m2, n. v0 ∈ vols ∧ m2 < # vols[v0] ∧ vols[v0][m2] ≠ unmapped ∧ vols[v, vols[v][m, ⌜vtblpnum1⌝ ]] = vols[v0, vols[v0][m2, ⌜n⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols) -- vols[v0][m2].pnum) ∧ apebs1[n].data = apebs[vols[v0][m2].pnum].data ∧ apebs1[n].fill ≤ apebs[vols[v0][m2].pnum].fill ∧ q1.lebrefs ⊆ q.lebrefs ++ (v0 × m2))))

User applied rule apply lemma

And obtained the following new goals

Proof step 96:
⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0)
Proof step 97:
# wlar0 = # wlar, # apebs = # wlar, # apebs1 = # wlar, avhdr.sqn = valid-sqns(v, m, apebs).max, valid-ebatbl(apebs, wlar, vols, vtblpnum4) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ vtblpnum4), apebs1[vtblpnum1] = mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), 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(aechdr(m1), avhdr, buf, m3, false), aehdr.valid?, m < # vols[v], vtblpnum1 < # wlar, vtblpnum2 < # wlar, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset1, wlar0), id(apebs1, apebs, mapped-pebs(vols)), id○(apebs1, apebs, vtblpnum1), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-inv(apebs1), ubi-io-peb-inv(mkpeb(aechdr(m1), avhdr, buf, m3, false)), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-ebatbl(apebs1, wlar0, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], vtblpnum), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs1, q1), valid-eraseq(wlar0, q1), valid-eraseq(q1), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum0), valid-peb(mkpeb(aechdr(m1), avhdr, buf, m3, false)), valid-peb(v, m, mkpeb(aechdr(m1), avhdr, buf, m3, false)), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), v ∈ vols, q1.lebrefs ⊆ q.lebrefs ++ (v × m), bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0, vols[v][m] ≠ unmapped → q1 = q + eq-entry(vols[v][m].pnum, v × m) ' ⊦ ⟪ubi_erase_worker_helper#(vtblpnum2; wlar0, apebs1; err); if err = ESUCCESS then q1 := q1.butlast⟫ ( # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum0) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0, q1) ∧ valid-eraseq(apebs1, q1) ∧ bflipset-cons(bflipset1, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], vtblpnum) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum) ∧ ubi-io-inv(apebs1) ∧ ( vols = vols[v, vols[v][m, ⌜vtblpnum1⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols[v, vols[v][m, ⌜vtblpnum1⌝ ]])) ∧ q1.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v0, m2, n. v0 ∈ vols ∧ m2 < # vols[v0] ∧ vols[v0][m2] ≠ unmapped ∧ vols[v, vols[v][m, ⌜vtblpnum1⌝ ]] = vols[v0, vols[v0][m2, ⌜n⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols) -- vols[v0][m2].pnum) ∧ apebs1[n].data = apebs[vols[v0][m2].pnum].data ∧ apebs1[n].fill ≤ apebs[vols[v0][m2].pnum].fill ∧ q1.lebrefs ⊆ q.lebrefs ++ (v0 × m2)))), vtblpnum4 = vtblpnum1, VTBL_VOLID ∈ vols, vtblpnum4 ∈ q, vtblpnum2 ∈ q, vtblpnum ∈ q1

Rule argument

spec: ubi-base name: valid-ebatbl seq: ⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0) subst: [apebs, wlar, vols, n0] → [apebs, wlar, vols, vtblpnum4]

Additional information

Used terms: apebs, wlar, vols, vtblpnum4