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Proof step 102 from proof inv-format (previous step)

# 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, range=(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 103:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 104:
# 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, EB_PAGE_SIZE + LEB_SIZE + EB_PAGE_SIZE ≤ # copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE) ∧ EB_PAGE_SIZE + LEB_SIZE + EB_PAGE_SIZE ≤ # emptypeb ∧ (∀ n. n < LEB_SIZE + EB_PAGE_SIZE → copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE)[EB_PAGE_SIZE + n] = (emptypeb)[EB_PAGE_SIZE + n])

Rule argument

spec: array-splice, inst: buffer name: range-eq-ext seq: ⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n]) subst: [m, n1, buf0, n0, buf] → [LEB_SIZE + EB_PAGE_SIZE, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE)] flags: <all paths>

Additional information

Used terms: LEB_SIZE + EB_PAGE_SIZE, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE)