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Proof step 41 from proof encode-node (previous step)

# buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), # buf = n0 + n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf0 = # buf, # buf2 = # buf, NODE_HEADER_SIZE + n0 + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = node-size-headerless(nd) + n1, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n2 + node-size-headerless(nd), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf2, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1) = subarray(buf0, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), 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)), (n2 + node-size-headerless(nd)) + n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, 2 * NODE_HEADER_SIZE + n + n2 + node-size-headerless(nd) ≤ # buf ⊦ subarray(fill(buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), n2), 0, n) = subarray(buf, 0, n) ∧ subarray (fill(buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), n2), n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), n0) = subarray(buf, n + 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), n0) ∧ (∃ buf, buf1. subarray (copy (validtrailer, 0, fill(buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), n2), n + NODE_HEADER_SIZE + n2 + node-size-headerless(nd), NODE_HEADER_SIZE), n, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) = buf + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) ∧ n2 + node-size-headerless(nd) = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# 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), 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))), 2 * NODE_HEADER_SIZE + n + n2 + node-size-headerless(nd) ≤ # 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 ⊦ subarray(fill(buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), n2), 0, n) = subarray(buf, 0, n) ∧ subarray(fill(buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), n2), n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), n0) = subarray(buf, n + 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd), n0) ∧ (∃ buf, buf1. subarray (copy (validtrailer, 0, fill(buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), n2), n + NODE_HEADER_SIZE + n2 + node-size-headerless(nd), NODE_HEADER_SIZE), n, 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd)) = buf + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = n2 + node-size-headerless(nd))

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (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)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic