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Proof step 94 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), 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(buf0 + buf1, # buf0, 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 insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-append-elim-left0 seq: ⊦ n = # buf ∧ m ≤ # buf0 → subarray(buf + buf0, n, m) = subarray(buf0, 0, m) subst: [m, n, buf0, buf] → [ 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf0, buf1, buf0] flags: <all paths>

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic Used terms: 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf0, buf1, buf0