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Proof step 249 from proof inv-recover (previous step)

# apebs0 = # wlar, # wlar1 = # wlar, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(vtblpnum1, avhdr.sqn), apebs0[vtblpnum1] = mkpeb(aehdr, avhdr, buf1, m0, boolvar), nx < # wlar, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset, wlar), indices-erasing(wlar, nx), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols1, vtblpnum1), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs0, q1), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, vtblpnum5), valid-global-sqn(apebs0, sqnum), valid-recs(apebs0, wlar, recs0), valid-recs-sqns(apebs0, recs0), valid-vtbl(apebs0, vols1, wlar1, vtblpnum1), valid-wl(apebs0, wlar1), valid-wl(apebs0, wlar), VTBL_VOLID × VTBL_LNUM ∈ recs0 ⊦ dups(nx), vtblpnum1 ∈ q1, VTBL_VOLID ∈ vols1, vtblpnum1 ∈ q, vtblpnum1 < # wlar ∧ ¬ boolvar

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] → [vtblpnum1, wlar1, vols1, apebs0] flags: <all paths>

Additional information

Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb);%lf-valid-wl-bad: n < # wlar ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, true) ∧ valid-wl(apebs, wlar) → wlar[n].status = erroneous;% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ used ≠ erroneous; (s) Used terms: vtblpnum1, wlar1, vols1, apebs0