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Proof step 86 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-echdr(subarray(buf, 0, EB_PAGE_SIZE), aechdr(n)) ∧ 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 87:
⊦ abs-echdr(buf, aehdr) ↔ (aehdr = empty → buf = emptypage) ∧ (aehdr.valid? → is-encoded(echdr(aehdr.ec), buf)) ∧ (aehdr = garbage → is-garbage-ec(buf) ∧ buf ≠ emptypage)
Proof step 88:
# 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 ⊦ ( (aechdr(n) = empty → subarray(buf, 0, EB_PAGE_SIZE) = emptypage) ∧ (aechdr(n).valid? → is-encoded(echdr(aechdr(n).ec), subarray(buf, 0, EB_PAGE_SIZE))) ∧ (aechdr(n) = garbage → is-garbage-ec(subarray(buf, 0, EB_PAGE_SIZE)) ∧ subarray(buf, 0, EB_PAGE_SIZE) ≠ emptypage)) ∧ abs-vidhdr(subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE), empty) ∧ subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkempbuf(LEB_SIZE)

Rule argument

spec: ubi-io-abs name: abs-echdr seq: ⊦ abs-echdr(buf, aehdr) ↔ (aehdr = empty → buf = emptypage) ∧ (aehdr.valid? → is-encoded(echdr(aehdr.ec), buf)) ∧ (aehdr = garbage → is-garbage-ec(buf) ∧ buf ≠ emptypage) subst: [aehdr, buf] → [aechdr(n), subarray(buf, 0, EB_PAGE_SIZE)] flags: <all paths>

Additional information

Used terms: aechdr(n), subarray(buf, 0, EB_PAGE_SIZE)