Proof step e-196b2df06b390016

parent_provers paper_theorem → concludes about Triangle T(n,k) = T(n-1,k) + 3*T(n-3,k-1) for k = 0..floor(n/3) 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 1993c1b537714cd17a68b6b46cc12de0374404ca921288ee874e92ac86660ffe, 2,282 bytes (969 compressed); download JSON

Cited by

• n-a4ffad71e3e1c62c (real_rooted)
• n-a4ffad71e3e1c62c (one_signed_coefficients)
• n-a4ffad71e3e1c62c (hadamard_kernel)
• n-a4ffad71e3e1c62c (interlacing)