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Proof step 258 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)) ∧ 0 = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs1[vtblpnum2, mkpeb(aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false)]).max

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: sqns name: valid-sqns-write seq: ⊦ n < # apebs → valid-sqns(v, m, apebs[n, apeb]) = ( valid-sqns(v, m, apebs) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅) subst: [apeb, n, apebs, m, v] → [mkpeb (aechdr(m0), avidhdr(VTBL_VOLID, VTBL_LNUM, 0, 0, 0), buf, LEB_SIZE, false), vtblpnum2, apebs1, 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), vtblpnum2, apebs1, VTBL_LNUM, VTBL_VOLID