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Proof step 64 from proof inv-write (previous step)

# apebs0 = # wlar, # apebs1 = # wlar, wlar[m0] = wl-entry(m1, used), apebs1[m0] = mkpeb(aehdr, avhdr, buf2, m, false), vols[v][vtblpnum4] = ⌜m0⌝ , apebs0[m0].bad, vtblpnum4 < # vols[v], m0 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(vtblpnum3, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs1), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m, false)), unique-sqns(apebs0), unique-sqns(apebs1), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-ebatbl(apebs1, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(apebs1, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs1, sqnum), valid-peb(v, vtblpnum4, apebs0[m0]), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(mkpeb(aehdr, avhdr, buf2, m, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-vtbl(apebs1, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), valid-wl(apebs1, wlar), v ∈ vols, m ≤ LEB_SIZE, vtblpnum3 ≤ LEB_SIZE, vtblpnum3 + n2 ≤ LEB_SIZE, n1 + n2 ≤ # buf, m ≤ vtblpnum3 ⊦ err = ESUCCESS, m0 = vtblpnum1, n2 = 0, m0 ∈ q, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs0[m0], aehdr0, avhdr0, buf0, m2, boolvar]

Additional information

Used simplifier rules: lf-valid-wl-bad: n < # wlar ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, true) ∧ valid-wl(apebs, wlar) → wlar[n].status = erroneous;%lf-valid-wl-not-erroneous: n < # wlar, stat ≠ erroneous ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ wlar[n] = wl-entry(m0, stat) ∧ valid-wl(apebs, wlar) → ¬ boolvar;%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; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ used ≠ erroneous; (s)%⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs0[m0], aehdr0, avhdr0, buf0, m2, boolvar