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Proof step 155 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf6 = NODE_HEADER_SIZE, # buf5 = a0.alignedsize, # buf3 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = a0.alignedsize, buf3 + subarray(buf0 + validtrailer, 0, n0) = buf6 + (buf5 + validtrailer) + buf2, n0 < NODE_HEADER_SIZE + a0.alignedsize, abs-node(buf1, a), abs-nodes (buf2, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0 + a ', lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', boolvar), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0, lax0, false), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), is-encoded(a0, subarray(buf5, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf6), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1 = n0, buf3 + buf0 + validtrailer = mkbuf(0), buf6 + buf5 + validtrailer = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [buf6 + (buf5 + validtrailer) + buf2, buf3 + subarray(buf0 + validtrailer, 0, n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ m + m = 2 * m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)% ⊦ m0 * 1 = m0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ m + n < m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m ≤ 0 ↔ m = 0; (s)% ⊦ n + 0 = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m + n = m + n0 ↔ n = n0; (s) Used terms: buf6 + (buf5 + validtrailer) + buf2, buf3 + subarray(buf0 + validtrailer, 0, n0)