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Proof step 111 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, abs-nodes(subarray(buf0, 0, n0), 2 * NODE_HEADER_SIZE + m + # buf, x, lax, true), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n0 ≤ # buf0, x ⊑ nd ' + x1, lax ⊑ @(m0, m1) ' + lax0, ∀ buf3, m, x, lax, n. # buf3 < #((buf2 + buf + validtrailer) + buf0) → abs-nodes(buf3, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf3 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf3, 0, n), m, x0, lax0, true)) ⊦ abs-nodes(((buf2 + buf) + validtrailer) + subarray(buf0, 0, n0), m, x, lax, true)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: abs-nodes-padding-prefix seq: ⊦ abs-padding(buf0) → ( abs-nodes(buf0 + buf1, m, x, lax, weak) ↔ abs-nodes(buf1, m + # buf0, x, lax, weak)) subst: [weak, lax, x, m, buf1, buf0] → [true, lax, x, m, subarray(buf0, 0, n0), (buf2 + buf) + validtrailer] flags: <all paths>

Additional information

Used simplifier rules: abs-nodes-unique-weak-h: ⊦ abs-nodes(buf, m, x0, lax0, true) → (abs-nodes(buf, m, x1, lax1, true) ↔ x0 = x1 ∧ lax0 = lax1);%abs-nodes-unique-weak-h: ⊦ abs-nodes(buf, m, x0, lax0, true) → (abs-nodes(buf, m, x1, lax1, true) ↔ x0 = x1 ∧ lax0 = lax1);% ⊦ #(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% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%⊦ is-encoded(nodeheader(# buf0, true), buf1) ∧ is-aligned(# buf0, 2 * NODE_HEADER_SIZE) → abs-padding(buf1 + buf0 + validtrailer); (ss)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: true, lax, x, m, subarray(buf0, 0, n0), (buf2 + buf) + validtrailer