Proof step e-0a3074c9769bc3e5

parent_provers paper_theorem → concludes about Triangle T(n,k) = n!/(k!*(n-3*k)!), for n >= 3*k >= 0, read by rows. JSON

Theorem

Parent-row provers of polytool polytool ?

Operation

Shared parent provers on the node's own rule

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

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "previous_interlaces_next" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: parent_provers, SHA-256 223f996ee01c9dd6a6bdc1a82bdad87f21351071cb6ddffb95930d754055601f, 2,137 bytes (908 compressed); download JSON

Cited by

• n-b12c32f9a9e37f0c (real_rooted)
• n-b12c32f9a9e37f0c (one_signed_coefficients)
• n-b12c32f9a9e37f0c (hadamard_kernel)
• n-b12c32f9a9e37f0c (interlacing)