Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes
shift_x_plus_one of basis_map_A013609 of Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k).
Premises
Theorem
polytool ?
Lean
RealRooted route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-bef0eb84bbabdca8 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
preserver_image, SHA-256 eb8dd3f04676c3c9365d119f6809066e253844b98ea5d5c7d7051a1e4f8e3145, 7,915 bytes (2,321 compressed); download
polytool replayed the certificate when the step was written.
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