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Proof step 243 from proof inv-format (previous step)

# buf1 = LEB_SIZE, # wlar = # apebs1, apebs1[vtblpnum2] = mkpeb(aehdr, empty, buf0, 0, false), wlar[vtblpnum2] = wl-entry(m, stat), aehdr.valid?, vtblpnum2 < # apebs1, is-aligned(LEB_SIZE, EB_PAGE_SIZE), is-encoded(∅, buf1), ubi-io-initial(apebs1), ubi-io-inv(apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)]), ubi-io-inv(apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf0, 0, false)]), ENCODED_NAT_SIZE ≤ LEB_SIZE, ∀ n3. n3 < # apebs1 → (apebs1[n3].bad → wlar[n3] = wl-entry(0, erroneous)) ∧ (¬ apebs1[n3].bad → apebs1[n3].echdr.valid? ∧ wlar[n3] = wl-entry(apebs1[n3].echdr.ec, free) ∧ apebs1[n3].vidhdr = empty) ⊦ vtblpnum2 = # apebs1, valid-wl(apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)], wlar[vtblpnum2, wl-entry(m, used)])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-wl seq: ⊦ valid-wl(apebs, wlar) ↔ (∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ ( wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max))) subst: [wlar, apebs] → [wlar[vtblpnum2, wl-entry(m, used)], apebs1 [vtblpnum2, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false) ]] flags: <all paths>

Additional information

Used terms: wlar[vtblpnum2, wl-entry(m, used)], apebs1 [vtblpnum2, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false) ]