Proof step e-7b49ab4fc0b1a646

parent_provers paper_theorem → concludes about Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 3 * T(n-4,k-1) for k = 0..floor(n/4); T(n,k)=0 for n or k < 0. 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 b56507a83aad54de3e9dd8bd42a97140db73b2e682502b0986b88741a4764488, 2,288 bytes (969 compressed); download JSON

Cited by

• n-a2db6b6ded7a955c (real_rooted)
• n-a2db6b6ded7a955c (one_signed_coefficients)
• n-a2db6b6ded7a955c (hadamard_kernel)
• n-a2db6b6ded7a955c (interlacing)