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Proof step 100 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), 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, n + n1 < # subarray(buf2, 0, n + NODE_HEADER_SIZE + node-size-headerless(nd)) + # fill(mkbuf(n2), empty), 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 ⊦ (n + n1 < # subarray(buf2, 0, n + NODE_HEADER_SIZE + node-size-headerless(nd)) ⊃ subarray(buf2, 0, n + NODE_HEADER_SIZE + node-size-headerless(nd))[n + n1] ;fill(mkbuf(n2), empty)[n + n1 - # subarray(buf2, 0, n + NODE_HEADER_SIZE + node-size-headerless(nd))] ) = (n1 < NODE_HEADER_SIZE ⊃ buf0[n + n1] ;((subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer)[n1 - NODE_HEADER_SIZE] )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 101:
# 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), 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 ⊦ (n1 < NODE_HEADER_SIZE + node-size-headerless(nd) ⊃ subarray(buf2, 0, n + NODE_HEADER_SIZE + node-size-headerless(nd))[n + n1] ;fill(mkbuf(n2), empty)[n1 - NODE_HEADER_SIZE + node-size-headerless(nd)] ) = (n1 < NODE_HEADER_SIZE ⊃ buf0[n + n1] ;((subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer)[n1 - NODE_HEADER_SIZE] )

Rule argument

Additional information

Used simplifier rules: ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ # fill(buf, d) = # buf; (s)% ⊦ m + n - n + n1 = m - n1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ # subarray(buf, m, n) = n; (s)