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Proof step 36 from proof abs-nodes-notrailer-h (previous step)

# buf2 = NODE_HEADER_SIZE, # buf = nd.alignedsize, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + n + nd.alignedsize, x0, lax0, weak), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize + # buf0 ⊦ subarray((buf2 + buf + validtrailer) + buf0, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE) = validtrailer, (NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + NODE_HEADER_SIZE ≤ #(buf2 + buf + validtrailer)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, nd.alignedsize < node-size-headerless(nd), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + n + nd.alignedsize, x0, lax0, weak), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize + # buf0 ⊦ subarray((buf2 + buf + validtrailer) + buf0, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE) = validtrailer

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%n ≠ 0, is-aligned(m, n) ⊦ m < align↑(m0, n) ↔ m < m0; (s)% ⊦ is-aligned(nd.alignedsize, 2 * NODE_HEADER_SIZE); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m = 2 * m; (s)