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Proof step 102 from proof inv-wl-worker (previous step)

# apebs1 = # wlar, # apebs = # wlar, # wlar0 = # wlar, avhdr.sqn = valid-sqns(v, m, apebs).max, apebs[vtblpnum4] = mkpeb(aechdr(m1), avhdr, buf, m3, false), apebs[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[vtblpnum4] = 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), vols[v][m] ≠ ⌜vtblpnum4⌝ , vtblpnum4 ≠ vtblpnum1, aehdr.valid?, vtblpnum1 < # wlar, m < # vols[v], vtblpnum4 < # 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(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), ¬ vtblpnum ∈ q1, ¬ vtblpnum4 ∈ q, ¬ VTBL_VOLID ∈ vols, vols[v][m] ≠ unmapped → q1 = q + eq-entry(vols[v][m].pnum, v × m) ', bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0 ⊦ ⟪ubi_erase_worker_helper#(vtblpnum4; 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 insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-vtbl seq: ⊦ valid-vtbl(apebs, vols, wlar, n0) ↔ n0 < # apebs ∧ n0 < # wlar ∧ wlar[n0].status = used ∧ apebs[n0].vidhdr.vol = VTBL_VOLID ∧ apebs[n0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[n0].data) subst: [n0, wlar, vols, apebs] → [vtblpnum4, wlar, vols, apebs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)% ⊦ wl-entry(m, stat).status = stat; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s) Used terms: vtblpnum4, wlar, vols, apebs