[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 89 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)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(pebs), ubi-io-initial(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ abs-vidhdr(subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE), empty) ∧ subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkempbuf(LEB_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 90:
⊦ abs-vidhdr(buf, avhdr) ↔ (avhdr = empty → buf = emptypage) ∧ (avhdr.valid? → is-encoded(vidhdr(avhdr.vol, avhdr.leb, avhdr.sqn, avhdr.size, avhdr.checksum), buf)) ∧ (avhdr = garbage → is-garbage-vid(buf) ∧ buf ≠ emptypage)
Proof step 91:
# 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)), 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 ⊦ ( (empty = empty → subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE) = emptypage) ∧ (empty.valid? → is-encoded(vidhdr(empty.vol, empty.leb, empty.sqn, empty.size, empty.checksum), subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE))) ∧ (empty = garbage → is-garbage-vid(subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE)) ∧ subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE) ≠ emptypage)) ∧ subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkempbuf(LEB_SIZE)

Rule argument

spec: ubi-io-abs name: abs-vidhdr seq: ⊦ abs-vidhdr(buf, avhdr) ↔ (avhdr = empty → buf = emptypage) ∧ ( avhdr.valid? → is-encoded (vidhdr (avhdr.vol, avhdr.leb, avhdr.sqn, avhdr.size, avhdr.checksum), buf)) ∧ (avhdr = garbage → is-garbage-vid(buf) ∧ buf ≠ emptypage) subst: [avhdr, buf] → [empty, subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE)] flags: <all paths>

Additional information

Used terms: empty, subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE)