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Proof step 118 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), n1 < NODE_HEADER_SIZE + node-size-headerless(nd) + n2, 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))), 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 ⊦ 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] ), n1 < NODE_HEADER_SIZE + node-size-headerless(nd)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 119:
# 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), n1 < NODE_HEADER_SIZE + node-size-headerless(nd) + n2, 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) ≤ 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 ⊦ fill(mkbuf(n2), empty)[n1 - NODE_HEADER_SIZE + node-size-headerless(nd)] = ((subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer)[n1 - NODE_HEADER_SIZE], n2 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m < (* m1) * m + n0 ↔ (m1 - 1) * m + n0 ≠ 0; (s)% ⊦ ¬ m + n < m; (s)% ⊦ m +1 = m + 1; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 2 * NODE_HEADER_SIZE + n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (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)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)