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Proof step 40 from proof inv-read (previous step)

# apebs = # wlar, vols[v][vtblpnum4] = ⌜m⌝ , wlar[m] = wl-entry(m0, used), apebs[m].bad, m < # wlar, vtblpnum4 < # vols[v], bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum5), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-peb(v, vtblpnum4, apebs[m]), valid-vtbl(apebs, vols, wlar, vtblpnum5), valid-wl(apebs, wlar), v ∈ vols, vtblpnum3 + n ≤ LEB_SIZE, n0 + n ≤ # buf ⊦ m = vtblpnum5, VTBL_VOLID ∈ vols, vtblpnum5 ∈ q, m ∈ 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] → [apebs[m], aehdr, avhdr, buf0, m1, 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: apebs[m], aehdr, avhdr, buf0, m1, boolvar