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Proof step 105 from proof inv-format (previous step)

# pebs0 = n + m1, # pebs1 = n + m1, # buf1 = EB_PAGE_SIZE, pebs1[m1] = mkpeb(buf0, m2, false), n0 < LEB_SIZE + EB_PAGE_SIZE, 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 ⊦ copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE)[EB_PAGE_SIZE + n0] = empty, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-copy, inst: buffer name: at-copy seq: ⊦ m0 < # buf → copy(buf0, n, buf, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ buf[m0];buf0[m0 + n - n0]) subst: [m0, m, n0, buf, n, buf0] → [EB_PAGE_SIZE + n0, EB_PAGE_SIZE, 0, emptypeb, 0, buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ m < 0; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ # emptypeb = PEB_SIZE; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%n < # emptypeb ⊦ (emptypeb)[n] = empty; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ PEB_SIZE ≤ EB_PAGE_SIZE + n → ¬ n < LEB_SIZE + EB_PAGE_SIZE; (s)%# buf = m, # buf0 = m ⊦ copy(buf, 0, buf0, 0, m) = buf; (s) Used terms: EB_PAGE_SIZE + n0, EB_PAGE_SIZE, 0, emptypeb, 0, buf1