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Proof step 101 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), ubi-io-initial(apebs), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE, ∀ n2. n2 < LEB_SIZE + EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n2] = empty ⊦ (n0 < EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n0] = empty) ∧ (n1 < LEB_SIZE → buf[2 * EB_PAGE_SIZE + n1] = empty)

User applied rule case distinction

And obtained the following new goals

Proof step 102:
# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < EB_PAGE_SIZE, abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), ubi-io-initial(pebs), ubi-io-initial(apebs), EB_PAGE_SIZE ≤ PEB_SIZE, ∀ n2. n2 < LEB_SIZE + EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n2] = empty ⊦ buf[EB_PAGE_SIZE + n0] = empty
Proof step 104:
# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n1 < LEB_SIZE, abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), ubi-io-initial(pebs), ubi-io-initial(apebs), EB_PAGE_SIZE ≤ PEB_SIZE, ∀ n2. n2 < LEB_SIZE + EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n2] = empty ⊦ buf[2 * EB_PAGE_SIZE + n1] = empty

Rule argument

pos: right 1

Proof step 101 from proof initial-ex-abstract-initial (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information