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Proof step 142 from proof inv-format (previous step)

# pebs = n0 + m1, # pebs0 = n0 + m1, pebs[m1] = mkpeb(buf, m, true), mtd-cons(pebs), mtd-cons(pebs0), ubi-io-initial(subarray(pebs, 0, m1)), n ≤ m1 ⊦ n0 = 0, ubi-io-peb-initial(subarray(pebs, 0, m1 + 1)[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 143:
⊦ ubi-io-initial(pebs) ↔ (∀ n. n < # pebs → ubi-io-peb-initial(pebs[n]))
Proof step 144:
# pebs0 = n0 + m1, # pebs = n0 + m1, pebs[m1] = mkpeb(buf, m, true), mtd-cons(pebs0), mtd-cons(pebs), n ≤ m1, ∀ n. n < # subarray(pebs, 0, m1) → ubi-io-peb-initial(subarray(pebs, 0, m1)[n]) ⊦ n0 = 0, ubi-io-peb-initial(subarray(pebs, 0, m1 + 1)[n])

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(pebs, 0, m1)] flags: <all paths>

Additional information

Used terms: subarray(pebs, 0, m1)