Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes
shift_x_plus_one of shift_x_plus_one of Triangle read by rows: T(n,k) is the number of Schroeder paths of length 2n and having k weak ascents (1<=k<=n). A Schr…
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-2c7c6c8ed6291ecb · 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 ca5af14f014f95918dff72d1ca10b89f7d11e3b578e174d8eed69161b5056995, 8,402 bytes (2,554 compressed); download
polytool replayed the certificate when the step was written.
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