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Proof step 42 from proof prepost-encode-orphans (previous step)

# buf = n0 + m0, is-aligned(n0 + m0, EB_PAGE_SIZE), is-encoded(orphans2, subarray(buf, 0, m0)), m0 ≤ LEB_SIZE, n0 + m0 ≤ LEB_SIZE, # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE ⊦ buf = subarray(buf, 0, m0) + subarray(buf, m0, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-append-consec0 seq: ⊦ n0 + n1 ≤ # buf → subarray(buf, 0, n0) + subarray(buf, n0, n1) = subarray(buf, 0, n0 + n1) subst: [n1, n0, buf] → [n0, m0, buf] flags: <all paths>

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m = m + n ↔ n = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)% ⊦ buf + buf0 = buf ↔ # buf0 = 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ m < n → ¬ n < m; (s) Used terms: n0, m0, buf