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Proof step 6 from proof abs-padding-subarray-failed (previous step)

# buf0 = NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + # buf1, is-aligned(# buf1, 2 * NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf1, true), buf0) ⊦ n = 0, ∃ buf2, buf3. subarray(buf0 + buf1 + validtrailer, 0, n) = buf2 + buf3 ∧ # buf2 = NODE_HEADER_SIZE ∧ (is-garbage-header(buf2) ∨ (∃ ndhd. is-encoded(ndhd, buf2) ∧ # buf3 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-append-shift-right seq: ⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf) subst: [m, buf0, buf] → [n, buf1 + validtrailer, buf0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → m ≤ n; (s) Used terms: n, buf1 + validtrailer, buf0