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Proof step 87 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), 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 ⊦ subarray ((subarray(buf2, 0, n + NODE_HEADER_SIZE + node-size-headerless(nd)) + fill(mkbuf(n2), empty)) + validtrailer, n, 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd)) = subarray(buf0, n, NODE_HEADER_SIZE) + (subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)) ∧ is-encoded(nd, subarray(subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2), 0, node-size-headerless(nd))) ∧ #(subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) = n2 + node-size-headerless(nd)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
# 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))), 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 ⊦ subarray ((subarray(buf2, 0, n + NODE_HEADER_SIZE + node-size-headerless(nd)) + fill(mkbuf(n2), empty)) + validtrailer, n, 2 * NODE_HEADER_SIZE + n2 + node-size-headerless(nd)) = subarray(buf0, n, NODE_HEADER_SIZE) + (subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd)) + mkempbuf(n2)) + validtrailer

Rule argument

Additional information

Used simplifier rules: 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)% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ is-encoded(nd, buf) → (is-encoded(nd0, buf) ↔ nd = nd0); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)