Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 1

Concludes
Triangle of Eulerian numbers T(n,k), 0 <= k <= n, read by rows.
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-93ffe46798ed877c · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 1,
  "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 d4d8a9099f230d666110001c13af088752a37a4e71eec023f55703164ff994ee, 11,000 bytes (2,911 compressed); download
polytool replayed the certificate when the step was written.
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