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Proof step 127 from proof encode-node (previous step)

# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n2 + node-size-headerless(nd), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), subarray(buf2, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), NODE_HEADER_SIZE + n0 + n2) = subarray(buf0, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), NODE_HEADER_SIZE + n0 + n2), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2), n1 < 2 * NODE_HEADER_SIZE + node-size-headerless(nd) + n2, n1 < 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), NODE_HEADER_SIZE + node-size-headerless(nd) + n2 ≤ n1, n + NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf, (n + NODE_HEADER_SIZE + node-size-headerless(nd)) + n2 ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd) ≤ # buf, (n2 + node-size-headerless(nd)) + n + NODE_HEADER_SIZE ≤ # buf, 2 * NODE_HEADER_SIZE + n + n2 + node-size-headerless(nd) ≤ # buf ⊦ (validtrailer)[n1 - NODE_HEADER_SIZE + node-size-headerless(nd) + n2] = ((subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer)[n1 - NODE_HEADER_SIZE]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 128:
# buf = n0 + n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), # buf0 = # buf, # buf2 = # buf, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n2 + node-size-headerless(nd), n1 = n3 + NODE_HEADER_SIZE + node-size-headerless(nd) + n2, subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + NODE_HEADER_SIZE + n0 + n2), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf2, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), NODE_HEADER_SIZE + n0 + n2) = subarray(buf0, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), NODE_HEADER_SIZE + n0 + n2), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), n1 < 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), n1 < 2 * NODE_HEADER_SIZE + node-size-headerless(nd) + n2, is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), 2 * NODE_HEADER_SIZE + n + n2 + node-size-headerless(nd) ≤ # buf, (n2 + node-size-headerless(nd)) + n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, (n + NODE_HEADER_SIZE + node-size-headerless(nd)) + n2 ≤ # buf, n + NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf, NODE_HEADER_SIZE + node-size-headerless(nd) + n2 ≤ n1 ⊦ (validtrailer)[n3] = ((subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer)[n1 - NODE_HEADER_SIZE]

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [NODE_HEADER_SIZE + node-size-headerless(nd) + n2, n1, n3]

Additional information

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