Proof step e-0050d566ad712b7d

parent_provers paper_theorem → concludes about Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or 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 9512eddffa6eb79b68454c8f9d408750984a9487d8198b7dd9368d8d151b56c8, 2,276 bytes (967 compressed); download JSON

Cited by

• n-e189038e95d51606 (real_rooted)
• n-e189038e95d51606 (one_signed_coefficients)
• n-e189038e95d51606 (hadamard_kernel)
• n-e189038e95d51606 (interlacing)