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Proof step 170 from proof inv-recover (previous step)

# wlar = # wlar0, # wlar1 = # wlar0, # apebs0 = # wlar0, apebs0[m1] = mkpeb(aehdr, avhdr, buf1, m0, false), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m1, avhdr.sqn), wlar0[m1] = wl-entry(m, used), nx < # wlar0, m1 < # wlar0, bflipset-cons(bflipset2, wlar0), bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset1, wlar1), indices-erasing(wlar, nx), is-encoded(vtbl, buf1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m0, false)), unique-sqns(apebs0), unmapped-vols(vols0), valid-ebatbl(apebs0, wlar0, vols, m1), valid-ebatbl(apebs0, wlar1, vols1, m1), valid-eraseq(wlar0, q0), valid-eraseq(wlar, q), valid-eraseq(apebs0, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs0, vtbl, q0), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum5), valid-indices(wlar0, nx), valid-peb(mkpeb(aehdr, avhdr, buf1, m0, false)), valid-recs(apebs0, wlar, recs0), valid-recs-sqns(apebs0, recs0), valid-vtbl(apebs0, vols, wlar0, m1), valid-vtbl(apebs0, vols0, wlar, m1), valid-vtbl(apebs0, vols1, wlar1, m1), valid-vtbl-weak(apebs0, m1), valid-wl(apebs0, wlar0), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar1), VTBL_VOLID × VTBL_LNUM ∈ recs0, q ⊆ q0 ⊦ dups(nx), VTBL_VOLID ∈ vols1, m1 ∈ q, VTBL_VOLID ∈ vols0, m1 ∈ q1, VTBL_VOLID ∈ vols, m1 ∈ q0, m1 ∈ nx, avhdr.vol = VTBL_VOLID ∧ avhdr.leb = VTBL_LNUM

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 171:
⊦ valid-recs(apebs, wlar, recs) ↔ (∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb)
Proof step 172:
# apebs0 = # wlar0, # wlar1 = # wlar0, # wlar = # wlar0, wlar0[m1] = wl-entry(m, used), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m1, avhdr.sqn), apebs0[m1] = mkpeb(aehdr, avhdr, buf1, m0, false), m1 < # wlar0, nx < # wlar0, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset2, wlar0), indices-erasing(wlar, nx), is-encoded(vtbl, buf1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m0, false)), unique-sqns(apebs0), unmapped-vols(vols0), valid-ebatbl(apebs0, wlar1, vols1, m1), valid-ebatbl(apebs0, wlar0, vols, m1), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs0, q1), valid-eraseq(wlar, q), valid-eraseq(wlar0, q0), valid-eraseq-strong(apebs0, vtbl, q0), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, vtblpnum5), valid-global-sqn(apebs0, sqnum), valid-indices(wlar0, nx), valid-peb(mkpeb(aehdr, avhdr, buf1, m0, false)), valid-recs-sqns(apebs0, recs0), valid-vtbl(apebs0, vols1, wlar1, m1), valid-vtbl(apebs0, vols0, wlar, m1), valid-vtbl(apebs0, vols, wlar0, m1), valid-vtbl-weak(apebs0, m1), valid-wl(apebs0, wlar1), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0), VTBL_VOLID × VTBL_LNUM ∈ recs0, q ⊆ q0, ∀ ladr, m. ladr ∈ recs0 ∧ recs0[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs0 ∧ apebs0[m].vidhdr.vol = ladr.vol ∧ apebs0[m].vidhdr.leb = ladr.leb ⊦ dups(nx), m1 ∈ nx, m1 ∈ q0, VTBL_VOLID ∈ vols, m1 ∈ q1, VTBL_VOLID ∈ vols0, m1 ∈ q, VTBL_VOLID ∈ vols1, avhdr.vol = VTBL_VOLID ∧ avhdr.leb = VTBL_LNUM

Rule argument

spec: ubi-crash-recovery-base name: valid-recs seq: ⊦ valid-recs(apebs, wlar, recs) ↔ (∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb) subst: [recs, wlar, apebs] → [recs0, wlar, apebs0] flags: <all paths>

Additional information

Used terms: recs0, wlar, apebs0