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Proof step 82 from proof inv-recover (previous step)

# apebs0 = # wlar, # wlar1 = # wlar, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar1[vtblpnum1] = wl-entry(m, used), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(vtblpnum1, avhdr.sqn), apebs0[vtblpnum1] = mkpeb(aehdr, avhdr, buf1, m0, false), nx < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset, wlar), indices-erasing(wlar, nx), is-encoded(to-vtbl(vols1), buf1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m0, 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-recs(apebs0, wlar, recs0), valid-recs-sqns(apebs0, recs0), valid-wl(apebs0, wlar), VTBL_VOLID × VTBL_LNUM ∈ recs0, ∀ n. n < # wlar → (wlar1[n].status = erroneous ↔ apebs0[n].bad) ∧ (wlar1[n].status = free → apebs0[n].vidhdr = empty) ∧ (wlar1[n].status ≠ erroneous ∧ wlar1[n].status ≠ erasing → apebs0[n].echdr = aechdr(wlar1[n].ec)) ∧ (wlar1[n].status = used → (∃ v, m. valid-peb(v, m, apebs0[n]) ∧ apebs0[n].vidhdr.sqn = valid-sqns(v, m, apebs0).max)) ⊦ dups(nx), vtblpnum1 ∈ q, VTBL_VOLID ∈ vols1, vtblpnum1 ∈ q1, valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aehdr, avhdr, buf1, m0, false)) ∧ avhdr.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs0).max

User applied rule all left

And closed the goal!

Rule argument

pos: left 30 terms: vtblpnum1 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ used ≠ erroneous; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)% ⊦ used ≠ erasing; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ used ≠ free; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s) Used terms: vtblpnum1