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Proof step 115 from proof recovery (previous step)

# wlar = # wlar0, # apebs0 = # wlar0, # avols0[v] = # vols0[v], # vols[v] = # vols0[v], vols0[v][m] = ⌜n⌝ , apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), apebs0[unmapped.pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar), vols[v][m] = unmapped, avhdr.valid?, n < # wlar0, m < # vols0[v], bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m0, false)), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-eraseq(apebs0, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum0), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs0, wlar), v ∈ vols0, v ∈ vols, v ∈ avols0, eq-entry(n, v × m) ∈ q, q0.lebrefs ⊆ q.lebrefs, avols0[v][m] = erased → ¬ v × m ∈ q ⊦ avols0[v][m].mapped?, VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0, m0 ≤ LEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ range=(buf, m0, emptyleb, 0, LEB_SIZE - m0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 116:
⊦ ubi-io-peb-inv(apeb) ↔ # apeb.data = LEB_SIZE ∧ ( ¬ apeb.bad → (apeb.echdr = empty → apeb.vidhdr = empty) ∧ (apeb.echdr ≠ garbage ∧ apeb.vidhdr = empty → apeb.fill = 0) ∧ apeb.fill ≤ LEB_SIZE ∧ is-aligned(apeb.fill, EB_PAGE_SIZE) ∧ subarray(apeb.data, apeb.fill, LEB_SIZE - apeb.fill) = mkempbuf(LEB_SIZE - apeb.fill))
Proof step 117:
# mkpeb(aehdr, avhdr, buf, m0, false).data = LEB_SIZE, # vols[v] = # vols0[v], # avols0[v] = # vols0[v], # apebs0 = # wlar0, # wlar = # wlar0, vols[v][m] = unmapped, apebs0[unmapped.pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar), apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), vols0[v][m] = ⌜n⌝ , avhdr.valid?, m < # vols0[v], n < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs0, vtblpnum0), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0), eq-entry(n, v × m) ∈ q, v ∈ avols0, v ∈ vols, v ∈ vols0, q0.lebrefs ⊆ q.lebrefs, avols0[v][m] = erased → ¬ v × m ∈ q, ¬ mkpeb(aehdr, avhdr, buf, m0, false).bad → (mkpeb(aehdr, avhdr, buf, m0, false).echdr = empty → mkpeb(aehdr, avhdr, buf, m0, false).vidhdr = empty) ∧ ( mkpeb(aehdr, avhdr, buf, m0, false).echdr ≠ garbage ∧ mkpeb(aehdr, avhdr, buf, m0, false).vidhdr = empty → mkpeb(aehdr, avhdr, buf, m0, false).fill = 0) ∧ mkpeb(aehdr, avhdr, buf, m0, false).fill ≤ LEB_SIZE ∧ is-aligned(mkpeb(aehdr, avhdr, buf, m0, false).fill, EB_PAGE_SIZE) ∧ subarray (mkpeb(aehdr, avhdr, buf, m0, false).data, mkpeb(aehdr, avhdr, buf, m0, false).fill, LEB_SIZE - mkpeb(aehdr, avhdr, buf, m0, false).fill) = mkempbuf(LEB_SIZE - mkpeb(aehdr, avhdr, buf, m0, false).fill) ⊦ avols0[v][m].mapped?, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols, m0 ≤ LEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ range=(buf, m0, emptyleb, 0, LEB_SIZE - m0)

Rule argument

spec: ubi-io-inv name: peb-inv seq: ⊦ ubi-io-peb-inv(apeb) ↔ # apeb.data = LEB_SIZE ∧ ( ¬ apeb.bad → (apeb.echdr = empty → apeb.vidhdr = empty) ∧ ( apeb.echdr ≠ garbage ∧ apeb.vidhdr = empty → apeb.fill = 0) ∧ apeb.fill ≤ LEB_SIZE ∧ is-aligned(apeb.fill, EB_PAGE_SIZE) ∧ subarray(apeb.data, apeb.fill, LEB_SIZE - apeb.fill) = mkempbuf(LEB_SIZE - apeb.fill)) subst: [apeb] → [mkpeb(aehdr, avhdr, buf, m0, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, buf, m0, false)