Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013609

Concludes

basis_map_A013609 of (5,1) Pascal triangle.

Premises

(5,1) Pascal triangle.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-3ed75a9efa0942bd · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 2,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 65294d48824ed4cff1309c114e8ae8850335b77632df1af3ba3b3dc38944fdff, 10,659 bytes (2,351 compressed); download

polytool replayed the certificate when the step was written.

Cited by