Proof step e-0d3631d0f359c9ce

parent_provers paper_theorem → concludes about Irregular triangle read by rows: T(n,k) = binomial(n-k, k), n >= 0, 0 <= k <= floor(n/2); or, coefficients of (one version of) Fibonacci polynomials. 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 7246e07017856dd0042ba75dd9b9c3f0c39c1a8ece66c8ce940c365457cda5d3, 2,274 bytes (964 compressed); download JSON

Cited by

• n-75ccd0453a9b6cec (real_rooted)
• n-75ccd0453a9b6cec (one_signed_coefficients)
• n-75ccd0453a9b6cec (hadamard_kernel)
• n-75ccd0453a9b6cec (interlacing)