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Proof step 120 from proof encode-node (previous step)

# 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), 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 < NODE_HEADER_SIZE + node-size-headerless(nd) + n2, 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) ≤ n1 ⊦ fill(mkbuf(n2), empty)[n3] = ((subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer)[n1 - NODE_HEADER_SIZE], n2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 121:
# 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), 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), n3 < n2, n3 < NODE_HEADER_SIZE + 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 ⊦ empty = ((subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer)[n3 + node-size-headerless(nd)]

Rule argument

Additional information

Used simplifier rules: ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → fill(mkbuf(n), d)[m] = d; (s)% ⊦ m < n → n ≠ 0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m + n < (* m1) * m + n0 ↔ n < (m1 - 1) * m + n0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n - m = n; (s)