Proof step

Parent-row provers of polytool

Shared parent provers on the sequence's own rule root domain

Concludes: T(n, k) = Sum_{j=0..n-k} (-1)^j*binomial(n - k + 1, j)*(n - k + 1 - j)^n. Triangle read by rows, T(n, k) for 1 <= k <= n.
Premises: none: a direct theorem check
Theorem: polytool ?
Checked: polytool replayed · Lean not attempted

Technical details

Step id

e-3261e39445e2e488 · JSON

Operation

Shared parent provers on the sequence's own rule

{
  "operation": "parent_provers",
  "route": "root_domain"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

parent_provers, SHA-256 4049e4a27a4130f8fa64a3c292f6ade79249e58d5302799dff5b37ea776362b8, 1,725 bytes (749 compressed); download

polytool replayed the certificate when the step was written.

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