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Proof step 21 from proof crash-neutral-write-data-wl (previous step)

apebs[n2] = mkpeb(aehdr, avhdr, buf0, 0, false), n1 = align↑(datasize(buf, n1), EB_PAGE_SIZE), avhdr.valid?, aehdr.valid?, n2 < # apebs, ubi-io-inv(apebs), n1 ≤ # buf, n1 ≤ LEB_SIZE ⊦ apebs = apebs[n2, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], datasize(buf, n1) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ apebs = apebs0[n, apeb] ↔ # apebs0 = # apebs ∧ (∀ m. m < # apebs0 → apebs[m] = (n = m ⊃ apeb;apebs0[m]))
Proof step 23:
apebs[n2] = mkpeb(aehdr, avhdr, buf0, 0, false), n1 = align↑(datasize(buf, n1), EB_PAGE_SIZE), aehdr.valid?, avhdr.valid?, n2 < # apebs, ubi-io-inv(apebs), n1 ≤ LEB_SIZE, n1 ≤ # buf ⊦ datasize(buf, n1) = 0, # apebs = # apebs ∧ (∀ m. m < # apebs → apebs[m] = (n2 = m ⊃ mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false);apebs[m]))

Rule argument

spec: array, inst: apebs name: ext-rec seq: ⊦ apebs = apebs0[n, apeb] ↔ # apebs0 = # apebs ∧ (∀ m. m < # apebs0 → apebs[m] = (n = m ⊃ apeb;apebs0[m])) subst: [apeb, n, apebs0, apebs] → [mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false), n2, apebs, apebs] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false), n2, apebs, apebs