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Proof step 172 from proof encode-node (previous step)

# subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n3 + n0) = # subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n3 + n0), # buf = n0 + n + 2 * NODE_HEADER_SIZE + n3 + node-size-headerless(nd), # buf0 = # buf, # buf2 = # buf, 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(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 + n3 + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, ⌊err⌋ , ∀ n1. n1 < # subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n3 + n0) → subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n3 + n0)[n1] = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n3 + n0)[n1] ⊦ buf0[2 * NODE_HEADER_SIZE + n + node-size-headerless(nd) + n2 + n3] = buf[(n + 2 * NODE_HEADER_SIZE + n3 + node-size-headerless(nd)) + n2]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 173:
# 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), 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⌋ , ∀ n1. n1 < node-size-headerless(nd) + NODE_HEADER_SIZE + n3 + n0 → buf0[(n + NODE_HEADER_SIZE) + n1] = buf[(n + NODE_HEADER_SIZE) + n1] ⊦ 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: ⊦ 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)