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Proof step 97 from proof decode-node (previous step)

is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf1, 0, NODE_HEADER_SIZE)), is-encoded(nd, subarray(buf1, NODE_HEADER_SIZE, node-size-headerless(nd))), range=(buf1, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf1, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≤ # buf1, NODE_HEADER_SIZE ≤ # buf1, NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf1 ⊦ ∃ buf2, buf3. subarray(buf1, 0, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) = buf2 + buf3 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf2) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)

User applied rule apply lemma

And obtained the following new goals

Proof step 98:
⊦ n ≤ # buf → (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n)
Proof step 99:
is-encoded(nd, subarray(buf1, NODE_HEADER_SIZE, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf1, 0, NODE_HEADER_SIZE)), range=(buf1, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf1, NODE_HEADER_SIZE ≤ # buf1, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≤ # buf1, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf1, NODE_HEADER_SIZE ≤ # buf1 → (∃ buf0, buf2. buf1 = buf0 + buf2 ∧ # buf0 = NODE_HEADER_SIZE) ⊦ ∃ buf2, buf3. subarray(buf1, 0, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) = buf2 + buf3 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf2) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)

Rule argument

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

Additional information

Used terms: NODE_HEADER_SIZE, buf1