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Proof step 106 from proof inv-wl-worker (previous step)

# apebs1 = # wlar, # apebs = # wlar, # wlar0 = # wlar, vols[v][m] = ⌜vtblpnum2⌝ , 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), avhdr = avidhdr(v1, m4, m5, m6, m7), m5 = valid-sqns(v, m, apebs).max, avhdr.valid?, aehdr.valid?, vtblpnum1 < # wlar, m < # vols[v], vtblpnum2 < # wlar, 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(q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(wlar0, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(apebs1, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs1, sqnum0), valid-global-sqn(apebs, sqnum), valid-peb(mkpeb(aechdr(m1), avhdr, buf, m3, false)), valid-peb(v, m, 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, bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0 ⊦ ⟪ubi_erase_worker_helper#(vtblpnum2; wlar0, apebs1; err); q1 := q + eq-entry(vtblpnum2, v × m) '; 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) -- vtblpnum2) ++ 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)))), vtblpnum = vtblpnum2, vtblpnum2 = vtblpnum4, vtblpnum4 = vtblpnum1, VTBL_VOLID ∈ vols, vtblpnum4 ∈ q, vtblpnum2 ∈ q, vtblpnum ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 107:
# wlar0 = # wlar, # apebs = # wlar, # apebs1 = # wlar, 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), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), buf, m3, false), vols[v][m] = ⌜vtblpnum2⌝ , vtblpnum ≠ vtblpnum2, vtblpnum2 ≠ vtblpnum4, vtblpnum4 ≠ vtblpnum1, aehdr.valid?, vtblpnum2 < # wlar, m < # vols[v], vtblpnum1 < # 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(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), ubi-io-peb-inv(mkpeb(aechdr(m1), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), buf, m3, false)), 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, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(wlar0, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(q + eq-entry(vtblpnum2, v × m) '), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum0), valid-peb(v, m, mkpeb(aechdr(m1), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), buf, m3, false)), valid-peb(mkpeb(aechdr(m1), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), 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, ¬ vtblpnum ∈ q, ¬ vtblpnum2 ∈ q, ¬ vtblpnum4 ∈ q, ¬ VTBL_VOLID ∈ vols, bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0 ⊦ ⟪ubi_erase_worker_helper#(vtblpnum2; wlar0, apebs1; err); q1 := q + eq-entry(vtblpnum2, v × m) '; 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) -- vtblpnum2) ++ 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))))

Rule argument

Additional information

Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb);%lf-used-valid-peb: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ apebs[n] = apeb ∧ valid-wl(apebs, wlar) → valid-peb(apeb);% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)