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Proof step 169 from proof encode-node (previous step)

# buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), # buf = n0 + n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf0 = # buf, # buf2 = # buf, NODE_HEADER_SIZE + n0 + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = node-size-headerless(nd) + n1, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n3 + node-size-headerless(nd), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), n2 < n0, is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, node-size-headerless(nd) ≤ align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), ⌊err⌋ , NODE_HEADER_SIZE + n2 + n3 < n1 → buf2[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3] = buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3] ⊦ buf2[(n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + n2] = buf[(n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) + n2]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 170:
# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + n3 + node-size-headerless(nd), buf2[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3] = buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3], align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n3 + node-size-headerless(nd), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n3) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n3), n2 < n0, is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + n3 + node-size-headerless(nd) ≤ # buf, ⌊err⌋ ⊦ buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3] = buf[(n + 2 * NODE_HEADER_SIZE + n3 + node-size-headerless(nd)) + n2]

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0 ⊦ n0 ≤ align↑(n0, m); (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)