[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 126 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < m0, abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(apebs), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ n0 = m0, ubi-io-peb-initial(apebs[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 127:
⊦ ubi-io-initial(apebs) ↔ (∀ n. n < # apebs → ubi-io-peb-initial(apebs[n]))
Proof step 128:
# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < m0, abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE, ∀ n. n < # apebs → ubi-io-peb-initial(apebs[n]) ⊦ n0 = m0, ubi-io-peb-initial(apebs[n0])

Rule argument

spec: ubi-io-inv name: initial seq: ⊦ ubi-io-initial(apebs) ↔ (∀ n. n < # apebs → ubi-io-peb-initial(apebs[n])) subst: [apebs] → [apebs] flags: <all paths>

Additional information

Used terms: apebs