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Proof step 83 from proof encode-node (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), buf2[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n1 + n2] = buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n1 + n2], align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n2 + 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), n1 < n0, is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), n + NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf, (n + NODE_HEADER_SIZE + node-size-headerless(nd)) + n2 ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd) ≤ # buf, (n2 + node-size-headerless(nd)) + n + NODE_HEADER_SIZE ≤ # buf, 2 * NODE_HEADER_SIZE + n + n2 + node-size-headerless(nd) ≤ # buf, ∀ n3. n3 < node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2 → buf0[(n + NODE_HEADER_SIZE) + n3] = buf[(n + NODE_HEADER_SIZE) + n3] ⊦ buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n1 + n2] = buf[(n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd)) + n1]

Rule argument

Additional information

Used simplifier rules: ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ # subarray(buf, m, n) = n; (s)