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Proof step 91 from proof decode-node (previous step)

is-encoded(nd, subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf, n, NODE_HEADER_SIZE)), range=(buf, n + NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≤ # buf ⊦ ∃ buf0, buf1. subarray(buf, n, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: array-split1 seq: ⊦ n ≤ # buf → (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n) subst: [n, buf] → [n, buf]

Additional information

Used terms: n, buf