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Proof step 232 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-global-sqn(apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)], 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 233:
m < # apebs ⊦ valid-peb(apeb) ∧ valid-global-sqn(apebs, n) ∧ apeb.vidhdr.sqn < n → valid-global-sqn(apebs[m, apeb], n)
Proof step 234:
# 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, valid-global-sqn(apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)], 1), vtblpnum2 < # apebs1 ∧ valid-peb(mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)) ∧ valid-global-sqn(apebs1, 1) ∧ mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false).vidhdr.sqn < 1

Rule argument

spec: ubi-base name: valid-global-sqn-add-valid seq: m < # apebs ⊦ valid-peb(apeb) ∧ valid-global-sqn(apebs, n) ∧ apeb.vidhdr.sqn < n → valid-global-sqn(apebs[m, apeb], n) subst: [n, apeb, m, apebs] → [1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false), vtblpnum2, apebs1] flags: <all paths>

Additional information

Used terms: 1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false), vtblpnum2, apebs1