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Proof step 261 from proof inv-format (previous step)

# wlar = # apebs1, wlar[vtblpnum2] = wl-entry(m0, free), apebs1[vtblpnum2] = mkpeb(aechdr(m0), empty, buf0, 0, false), vtblpnum2 < # apebs1, is-aligned(LEB_SIZE, EB_PAGE_SIZE), is-encoded(∅, buf), ubi-io-initial(apebs1), ubi-io-inv(apebs1[vtblpnum2, mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false)]), ubi-io-inv(apebs1[vtblpnum2, mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf0, 0, false)]), ubi-io-peb-inv(mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false)), ENCODED_NAT_SIZE ≤ LEB_SIZE ⊦ vtblpnum2 = # apebs1, valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 262:
⊦ 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 263:
# wlar = # apebs1, apebs1[vtblpnum2] = mkpeb(aechdr(m0), empty, buf0, 0, false), wlar[vtblpnum2] = wl-entry(m0, free), vtblpnum2 < # apebs1, is-aligned(LEB_SIZE, EB_PAGE_SIZE), is-encoded(∅, buf), ubi-io-initial(apebs1), ubi-io-inv(apebs1[vtblpnum2, mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf0, 0, false)]), ubi-io-inv(apebs1[vtblpnum2, mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false)]), ubi-io-peb-inv(mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false)), ENCODED_NAT_SIZE ≤ LEB_SIZE ⊦ vtblpnum2 = # apebs1, ¬ mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false).bad ∧ mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false).echdr.valid? ∧ (∃ m3, m1, m2. mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false).vidhdr = avidhdr(VTBL_VOLID, VTBL_LNUM, m3, m1, m2) ∧ ( m1 ≠ 0 → m1 ≤ datasize(mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false).data) ∧ m2 = checksum(mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false).data, m1)))

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(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false), VTBL_LNUM, VTBL_VOLID] flags: <all paths>

Additional information

Used terms: mkpeb (aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false), VTBL_LNUM, VTBL_VOLID