Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 2

Concludes

Premises

Triangle read by rows. A generalization of unsigned Lah numbers, called L[4,1].
sequence: Every row P_n, n >= 3, 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-3f86cc05e6d83baf · JSON

Operation

Image under a real-rootedness preserver

{
  "index_shift": 2,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"-2\",\"intercept\":\"0\"}"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "lower": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

preserver_image, SHA-256 b21285a6fa36182c5459d95869afd26c8c6537222feef368d0558e0878aea40f, 12,536 bytes (2,899 compressed); download

polytool replayed the certificate when the step was written.

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