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Proof step 97 from proof inv-format (previous step)

# pebs0 = n + m1, # pebs1 = n + m1, # buf1 = EB_PAGE_SIZE, pebs1[m1] = mkpeb(buf0, m2, false), is-encoded(echdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)), buf1), mtd-cons(pebs0), mtd-cons(pebs1), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), mtd-cons(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)]), ubi-io-initial(subarray(pebs1, 0, m1)), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ n = 0, ubi-io-peb-initial(mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 98:
⊦ ubi-io-peb-initial(peb) ↔ mtd-valid-peb(peb) ∧ (¬ peb.bad → peb.fill = EB_PAGE_SIZE ∧ (∃ n. is-encoded(echdr(n), subarray(peb.data, 0, EB_PAGE_SIZE))))
Proof step 99:
# buf1 = EB_PAGE_SIZE, # pebs1 = n + m1, # pebs0 = n + m1, pebs1[m1] = mkpeb(buf0, m2, false), is-encoded(echdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)), buf1), mtd-cons(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)]), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), mtd-cons(pebs1), mtd-cons(pebs0), ubi-io-initial(subarray(pebs1, 0, m1)), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ n = 0, mtd-valid-peb(mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)) ∧ ( ¬ mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).bad → mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).fill = EB_PAGE_SIZE ∧ (∃ n. is-encoded(echdr(n), subarray(mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).data, 0, EB_PAGE_SIZE))))

Rule argument

spec: ubi-io-base name: ubi-io-peb-initial seq: ⊦ ubi-io-peb-initial(peb) ↔ mtd-valid-peb(peb) ∧ ( ¬ peb.bad → peb.fill = EB_PAGE_SIZE ∧ (∃ n. is-encoded (echdr(n), subarray(peb.data, 0, EB_PAGE_SIZE)))) subst: [peb] → [mkpeb (copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)] flags: <all paths>

Additional information

Used terms: mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)