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Proof step 64 from proof initial-ex-abstract-initial (previous step)

m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, m, false), abs(subarray(pebs, 0, m0), apebs), ubi-io-initial(pebs), ubi-io-initial(apebs) ⊦ ∃ apebs. abs(pebs, apebs) ∧ ubi-io-initial(apebs)

User applied rule apply lemma

And obtained the following new goals

Proof step 65:
⊦ ubi-io-initial(pebs) ↔ (∀ n. n < # pebs → ubi-io-peb-initial(pebs[n]))
Proof step 66:
m0 + 1 = # pebs, ubi-io-initial(pebs) ↔ (∀ n. n < # pebs → ubi-io-peb-initial(pebs[n])), pebs[m0] = mkpeb(buf, m, false), abs(subarray(pebs, 0, m0), apebs), ubi-io-initial(apebs), ubi-io-initial(pebs) ⊦ ∃ apebs. abs(pebs, apebs) ∧ ubi-io-initial(apebs)

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] → [pebs]

Additional information

Used terms: pebs