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Proof step 108 from proof inv-format (previous step)

# buf1 = EB_PAGE_SIZE, # pebs1 = n + m1, # pebs0 = n + m1, pebs1[m1] = mkpeb(buf0, m2, false), n0 < m1, n0 < n + m1, is-encoded(echdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)), buf1), mtd-cons(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)]), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), mtd-cons(pebs1), mtd-cons(pebs0), ubi-io-initial(subarray(pebs1, 0, m1)), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ n = 0, n0 = m1, ubi-io-peb-initial(pebs1[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 109:
⊦ ubi-io-initial(pebs) ↔ (∀ n. n < # pebs → ubi-io-peb-initial(pebs[n]))
Proof step 110:
# pebs0 = n + m1, # pebs1 = n + m1, # buf1 = EB_PAGE_SIZE, pebs1[m1] = mkpeb(buf0, m2, false), n0 < n + m1, n0 < m1, is-encoded(echdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)), buf1), mtd-cons(pebs0), mtd-cons(pebs1), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), mtd-cons(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)]), EB_PAGE_SIZE ≤ PEB_SIZE, ∀ n. n < # subarray(pebs1, 0, m1) → ubi-io-peb-initial(subarray(pebs1, 0, m1)[n]) ⊦ n = 0, n0 = m1, ubi-io-peb-initial(pebs1[n0])

Rule argument

spec: ubi-io-base name: ubi-io-initial seq: ⊦ ubi-io-initial(pebs) ↔ (∀ n. n < # pebs → ubi-io-peb-initial(pebs[n])) subst: [pebs] → [subarray(pebs1, 0, m1)] flags: <all paths>

Additional information

Used terms: subarray(pebs1, 0, m1)