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Proof step 246 from proof inv-format (previous step)

# wlar = # apebs1, # buf1 = LEB_SIZE, wlar[vtblpnum2] = wl-entry(m, stat), apebs1[vtblpnum2] = mkpeb(aehdr, empty, buf0, 0, false), aehdr.valid?, n < # apebs1, 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, ( wlar[vtblpnum2, wl-entry(m, used)][n].status = erroneous ↔ apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n].bad) ∧ (wlar[vtblpnum2, wl-entry(m, used)][n].status = free → apebs1[n].vidhdr = empty) ∧ ( wlar[vtblpnum2, wl-entry(m, used)][n].status ≠ erroneous ∧ wlar[vtblpnum2, wl-entry(m, used)][n].status ≠ erasing → apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n].echdr = aechdr(wlar[vtblpnum2, wl-entry(m, used)][n].ec)) ∧ ( wlar[vtblpnum2, wl-entry(m, used)][n].status = used → (∃ v, m. valid-peb(v, m, apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n]) ∧ apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n].vidhdr.sqn = valid-sqns(v, m, apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)]).max))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 247:
# buf1 = LEB_SIZE, # wlar = # apebs1, apebs1[vtblpnum2] = mkpeb(aehdr, empty, buf0, 0, false), wlar[vtblpnum2] = wl-entry(m, stat), apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n] = mkpeb(aehdr0, avhdr, buf, m0, boolvar), aehdr.valid?, vtblpnum2 < # apebs1, n < # 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, (wlar[vtblpnum2, wl-entry(m, used)][n].status = erroneous ↔ boolvar) ∧ (wlar[vtblpnum2, wl-entry(m, used)][n].status = free → apebs1[n].vidhdr = empty) ∧ ( wlar[vtblpnum2, wl-entry(m, used)][n].status ≠ erroneous ∧ wlar[vtblpnum2, wl-entry(m, used)][n].status ≠ erasing → aehdr0 = aechdr(wlar[vtblpnum2, wl-entry(m, used)][n].ec)) ∧ ( wlar[vtblpnum2, wl-entry(m, used)][n].status = used → (∃ v, m. valid-peb(v, m, apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)][n]) ∧ avhdr.sqn = valid-sqns(v, m, apebs1[vtblpnum2, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false)]).max))

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs1 [vtblpnum2, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false) ] [n ], aehdr0, avhdr, buf, m0, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs1 [vtblpnum2, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf1, LEB_SIZE, false) ] [n ], aehdr0, avhdr, buf, m0, boolvar