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Proof step 282 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-ebatbl (apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)], wlar[vtblpnum2, wl-entry(m, used)], ∅, vtblpnum2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 283:
⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0)
Proof step 284:
# wlar = # apebs1, # buf1 = LEB_SIZE, wlar[vtblpnum2] = wl-entry(m, stat), apebs1[vtblpnum2] = mkpeb(aehdr, empty, buf0, 0, false), 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), buf0, 0, false)]), ubi-io-inv(apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, 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, ∀ v, m0, n. (∅)[v][m0] = ⌜n⌝ ∧ v ∈ ∅ ∧ m0 < # (∅)[v] ↔ wlar[vtblpnum2, wl-entry(m, used)][n].status = used ∧ n < # apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)] ∧ n < # wlar[vtblpnum2, wl-entry(m, used)] ∧ apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n].vidhdr.valid? ∧ apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n].vidhdr.vol = v ∧ apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n].vidhdr.leb = m0 ∧ n ≠ vtblpnum2

Rule argument

spec: ubi-base name: valid-ebatbl seq: ⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0) subst: [n0, vols, wlar, apebs] → [vtblpnum2, ∅, 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: vtblpnum2, ∅, wlar[vtblpnum2, wl-entry(m, used)], apebs1 [vtblpnum2, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false) ]