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Proof step 74 from proof inv-recover (previous step)

# wlar1 = # wlar, # apebs0 = # wlar, apebs0[vtblpnum1] = mkpeb(aehdr, avhdr, buf1, m0, false), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(vtblpnum1, avhdr.sqn), vtblpnum1 < # wlar, nx < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar), indices-erasing(wlar, nx), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m0, false)), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols1, vtblpnum1), valid-eraseq(wlar, q), valid-eraseq(apebs0, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum5), valid-recs(apebs0, wlar, recs0), valid-recs-sqns(apebs0, recs0), valid-vtbl(apebs0, vols1, wlar1, vtblpnum1), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar1), VTBL_VOLID × VTBL_LNUM ∈ recs0 ⊦ dups(nx), vtblpnum1 ∈ q1, VTBL_VOLID ∈ vols1, vtblpnum1 ∈ q, valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aehdr, avhdr, buf1, m0, false)) ∧ avhdr.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs0).max ∧ (∃ vtbl. is-encoded(vtbl, buf1) ∧ ¬ VTBL_VOLID ∈ vtbl)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 75:
⊦ 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)
Proof step 76:
# apebs0 = # wlar, # wlar1 = # wlar, apebs0[vtblpnum1].vidhdr.leb = VTBL_LNUM, wlar1[vtblpnum1].status = used, apebs0[vtblpnum1].vidhdr.vol = VTBL_VOLID, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(vtblpnum1, avhdr.sqn), apebs0[vtblpnum1] = mkpeb(aehdr, avhdr, buf1, m0, false), vtblpnum1 < # apebs0, vtblpnum1 < # wlar1, nx < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset, wlar), indices-erasing(wlar, nx), is-encoded(to-vtbl(vols1), apebs0[vtblpnum1].data), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m0, false)), 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-wl(apebs0, wlar1), valid-wl(apebs0, wlar), VTBL_VOLID × VTBL_LNUM ∈ recs0 ⊦ dups(nx), vtblpnum1 ∈ q, VTBL_VOLID ∈ vols1, vtblpnum1 ∈ q1, valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aehdr, avhdr, buf1, m0, false)) ∧ avhdr.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs0).max ∧ (∃ vtbl. is-encoded(vtbl, buf1) ∧ ¬ VTBL_VOLID ∈ vtbl)

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 terms: vtblpnum1, wlar1, vols1, apebs0