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Proof step 147 from proof inv-wl-worker (previous step)

# apebs = # wlar, # wlar0 = # wlar, # apebs1 = # wlar, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, apebs1[vtblpnum1] = mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), wlar[vtblpnum1] = wl-entry(m0, free), wlar[vtblpnum4] = wl-entry(m1, used), apebs[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs[vtblpnum4] = mkpeb(aehdr1, avhdr, buf, m3, false), apebs2 = apebs1, wlar1 = wlar0, aehdr.valid?, vtblpnum4 < # wlar, 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(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(aehdr1, avhdr, buf, m3, false)), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs1, wlar0, vols, vtblpnum), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs1, q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(wlar0, q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum0), valid-peb(mkpeb(aehdr1, avhdr, buf, m3, false)), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0, ∀ v, m. ¬ v ∈ vols ∧ is-encoded(to-vtbl(vols)[v, m], buf) → valid-ebatbl(apebs1, wlar0, vols[v, fill(mkebatbl(m), unmapped)], vtblpnum) ∧ valid-vtbl(apebs1, vols[v, fill(mkebatbl(m), unmapped)], wlar0, vtblpnum) ⊦ ∀ wlar0, apebs1, err. ( err = ESUCCESS → # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum0) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(wlar0, q) ∧ valid-eraseq(apebs1, q) ∧ bflipset-cons(bflipset1, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols, vtblpnum) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum)) ∧ ( err ≠ ESUCCESS → # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum0) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(wlar0, q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-eraseq(apebs1, q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) ') ∧ bflipset-cons(bflipset1, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols, vtblpnum) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum)) ∧ ubi-io-inv(apebs1) ∧ wlar0[vtblpnum4].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar0, wlar1, vtblpnum4) ∧ id○(apebs1, apebs2, vtblpnum4) ∧ id(apebs1, apebs2, mapped-pebs(vols)) → ⟪q1 := q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '; 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, vtblpnum) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum) ∧ ( id(apebs1, apebs, mapped-pebs(vols)) ∧ q1.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] ≠ unmapped ∧ vols = vols[v, vols[v][m, ⌜n⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols) -- vols[v][m].pnum) ∧ apebs1[n].data = apebs[vols[v][m].pnum].data ∧ apebs1[n].fill ≤ apebs[vols[v][m].pnum].fill ∧ q1.lebrefs ⊆ q.lebrefs ++ (v × m)))), vtblpnum = vtblpnum4, vtblpnum4 = vtblpnum1, vtblpnum4 ∈ q, VTBL_VOLID ∈ vols, vtblpnum ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ id(apebs1, apebs0, ns) → id(apebs1, apebs0, ns -- n); (s)%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ns ∩ ns = ns; (s)%stat ≠ used ⊦ wlar[n] = wl-entry(m0, stat) ∧ valid-ebatbl(apebs, wlar, vols, m1) → mapped-pebs(vols) -- n = mapped-pebs(vols); (s)% ⊦ used ≠ free; (s)%idexcept-size: ⊦ id○(wlar, wlar0, n) → # wlar = # wlar0; (forward) from specification array-copy[wlarray-base]%idexcept-size: ⊦ id○(apebs, apebs0, n) → # apebs = # apebs0; (forward) from specification array-copy[apebs]%idset-trans-intersect: ⊦ id(apebs2, apebs1, ns0) ∧ id(apebs1, apebs0, ns1) → id(apebs2, apebs0, ns0 ∩ ns1); (forward) from specification ubi-base%idset-idexpt-fwd: ⊦ id(apebs2, apebs1, ns) ∧ id○(apebs1, apebs0, n) → id(apebs2, apebs0, ns -- n); (forward) from specification ubi-base