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Proof step 46 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m, apebs).max, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, vols[v][m] = unmapped, wlar[n1] = wl-entry(m4, used), wlar[n] = wl-entry(m5, erasing), wlar[n0] = wl-entry(m6, used), apebs[n1] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), apebs[n0] = mkpeb(aechdr(m6), avhdr1, buf1, m2, false), m < # vols[v], n < # wlar, n1 < # wlar, n0 < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr1, buf1, m2, false)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), v ∈ vols, ∀ v, m, n2. vols[v][m] = ⌜n2⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m ∧ n2 ≠ n0 ⊦ avhdr0.sqn = (valid-sqns(v, m, apebs) ++ avhdr.sqn).max, n1 = n, valid-peb(v, m, apebs[n]), VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ valid-peb(v, m, apeb) ↔ ¬ apeb.bad ∧ apeb.echdr.valid? ∧ (∃ m0, m1, m2. apeb.vidhdr = avidhdr(v, m, m0, m1, m2) ∧ (m1 ≠ 0 → m1 ≤ datasize(apeb.data) ∧ m2 = checksum(apeb.data, m1)))
Proof step 48:
# apebs = # wlar, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr0.sqn = valid-sqns(v, m, apebs).max, apebs[n0] = mkpeb(aechdr(m6), avhdr1, buf1, m2, false), apebs[n1] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), wlar[n0] = wl-entry(m6, used), wlar[n] = wl-entry(m5, erasing), wlar[n1] = wl-entry(m4, used), vols[v][m] = unmapped, mkpeb(aechdr(m6), avhdr1, buf1, m2, false).echdr.valid?, n0 < # wlar, n1 < # wlar, n < # wlar, m < # vols[v], is-encoded(to-vtbl(vols), buf1), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), v ∈ vols, ∀ v, m, n2. vols[v][m] = ⌜n2⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m ∧ n2 ≠ n0, ∃ m0, m1, m3. mkpeb(aechdr(m6), avhdr1, buf1, m2, false).vidhdr = avidhdr(VTBL_VOLID, VTBL_LNUM, m0, m1, m3) ∧ (m1 ≠ 0 → m1 ≤ datasize(mkpeb(aechdr(m6), avhdr1, buf1, m2, false).data) ∧ m3 = checksum(mkpeb(aechdr(m6), avhdr1, buf1, m2, false).data, m1)) ⊦ avhdr0.sqn = (valid-sqns(v, m, apebs) ++ avhdr.sqn).max, n1 = n, mkpeb(aechdr(m6), avhdr1, buf1, m2, false).bad, valid-peb(v, m, apebs[n]), VTBL_VOLID ∈ vols

Rule argument

spec: valid-peb name: valid-peb2 seq: ⊦ valid-peb(v, m, apeb) ↔ ¬ apeb.bad ∧ apeb.echdr.valid? ∧ (∃ m0, m1, m2. apeb.vidhdr = avidhdr(v, m, m0, m1, m2) ∧ ( m1 ≠ 0 → m1 ≤ datasize(apeb.data) ∧ m2 = checksum(apeb.data, m1))) subst: [apeb, m, v] → [mkpeb(aechdr(m6), avhdr1, buf1, m2, false), VTBL_LNUM, VTBL_VOLID] flags: <all paths>

Additional information

Used terms: mkpeb(aechdr(m6), avhdr1, buf1, m2, false), VTBL_LNUM, VTBL_VOLID