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Proof step 173 from proof encode-node (previous step)

# 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]

User applied rule all left

And closed the goal!

Rule argument

pos: left 14 terms: NODE_HEADER_SIZE + node-size-headerless(nd) + n2 + n3 abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + m = 2 * m; (s) Used terms: NODE_HEADER_SIZE + node-size-headerless(nd) + n2 + n3