Proof step e-3e082ac2cc139530

parent_provers root_domain → concludes about 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. JSON

Theorem

Parent-row provers of polytool polytool ?

Operation

Shared parent provers on the node's own rule

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

Premises

None: this step is a direct theorem check.

Claims

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

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: parent_provers, SHA-256 010f7ec5709036ef07871822c6586425465ded1a234d826be58545e42bda80e2, 1,590 bytes (711 compressed); download JSON

Cited by

• n-3b2b9e31bd278a34 (real_rooted)
• n-3b2b9e31bd278a34 (one_signed_coefficients)
• n-3b2b9e31bd278a34 (hadamard_kernel)