Proof step e-4d4f59f3aacb50cf

parent_provers paper_theorem → concludes about Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n). 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 069a9c6d44b2deacf635f30b1ab74840f840bb6248f5a135920e4123f2ec73fc, 2,199 bytes (901 compressed); download JSON

Cited by

• n-569a801b809b6abd (one_signed_coefficients)
• n-569a801b809b6abd (hadamard_kernel)
• n-569a801b809b6abd (interlacing)
• n-569a801b809b6abd (real_rooted)