Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes

Premises

derivative of Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Lean

RealRooted Polynomial.Splits.comp_of_degree_le_one

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-b5f432629a23a91c · JSON

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "-1"
    }
  }
}

Certificate

preserver_image, SHA-256 abf68aefd1ab324d2120fdc4d71072f3222f22e04e0f21a954c5bdc823fdd41c, 8,708 bytes (2,399 compressed); download

polytool replayed the certificate when the step was written.

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