[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 273 from proof inv-recover (previous step)

# wlar1 = # wlar, # apebs0 = # wlar, avhdr0.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs0).max, wlar[vtblpnum1] = wl-entry(m3, stat), wlar1[vtblpnum1] = wl-entry(m2, used), apebs0[vtblpnum1] = mkpeb(aechdr(m2), avhdr0, buf, m1, false), apebs0[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m, avhdr.sqn), vtblpnum1 < # wlar, nx < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset1, wlar1), indices-erasing(wlar, nx), is-encoded(to-vtbl(vols1), buf), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aechdr(m2), avhdr0, buf, m1, false)), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols1, vtblpnum1), valid-eraseq(wlar, q), valid-eraseq(apebs0, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum5), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m2), avhdr0, buf, m1, false)), valid-recs-sqns(apebs0, recs0), VTBL_VOLID × VTBL_LNUM ∈ recs0, ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs0[n].bad) ∧ (wlar[n].status = free → apebs0[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs0[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs0[n]) ∧ apebs0[n].vidhdr.sqn = valid-sqns(v, m, apebs0).max)) ⊦ m = vtblpnum1, stat = used, dups(nx), VTBL_VOLID ∈ vols1, vtblpnum1 ∈ q1, m ∈ q

User applied rule all left

And obtained the following new goals

Proof step 274:
# apebs0 = # wlar, # wlar1 = # wlar, avhdr0.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs0).max, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m, avhdr.sqn), apebs0[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), apebs0[vtblpnum1] = mkpeb(aechdr(m2), avhdr0, buf, m1, false), wlar1[vtblpnum1] = wl-entry(m2, used), wlar[vtblpnum1] = wl-entry(m3, stat), nx < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset, wlar), indices-erasing(wlar, nx), is-encoded(to-vtbl(vols1), buf), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aechdr(m2), avhdr0, buf, m1, false)), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols1, vtblpnum1), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs0, q1), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, vtblpnum5), valid-global-sqn(apebs0, sqnum), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m2), avhdr0, buf, m1, false)), valid-recs-sqns(apebs0, recs0), VTBL_VOLID × VTBL_LNUM ∈ recs0, vtblpnum1 < # wlar → (wlar[vtblpnum1].status = erroneous ↔ apebs0[vtblpnum1].bad) ∧ (wlar[vtblpnum1].status = free → apebs0[vtblpnum1].vidhdr = empty) ∧ (wlar[vtblpnum1].status ≠ erroneous ∧ wlar[vtblpnum1].status ≠ erasing → apebs0[vtblpnum1].echdr = aechdr(wlar[vtblpnum1].ec)) ∧ (wlar[vtblpnum1].status = used → (∃ v, m. valid-peb(v, m, apebs0[vtblpnum1]) ∧ apebs0[vtblpnum1].vidhdr.sqn = valid-sqns(v, m, apebs0).max)) ⊦ m = vtblpnum1, stat = used, dups(nx), m ∈ q, vtblpnum1 ∈ q1, VTBL_VOLID ∈ vols1

Rule argument

pos: left 29 terms: vtblpnum1 abort: F discard: T computed: T

Additional information

Used terms: vtblpnum1